Take a look at https://docs.gitlab.com/omnibus/settings/nginx.html#inserting-custom-nginx-settings-into-the-gitlab-server-block - add this to the server block

location ^~ /.well-known/acme-challenge/ {
  default_type "type/plain";
  root /tmp/letsencrypt;
}

issue this command
mkdir /tmp/letsencrypt

Restart Gitlab and then try and renew the SSL

.. or you can reconfigure gitlab to not use SSL

That is quite alright.

If you would like to give it a shot. (backup your Gitlab configuration file)

This is how I run my Gitlab installation - non-bundled NGINX webserver

http://www.creativespacesbysherihannah.com/wp-sys/wp-content/uploads/staircase-before.jpg?TB_iframe=true&width=700&height=351

You will need to install NGINX

wget https://nginx.org/keys/nginx_signing.key -O - | sudo apt-key add -

echo "deb http://nginx.org/packages/mainline/ubuntu/ xenial nginx
deb-src http://nginx.org/packages/mainline/ubuntu/ xenial nginx" > /etc/apt/sources.list.d/nginx.list

apt-get -y update

apt-get -y install nginx

this will install NGINX Mainline

My NGINX configuration looks like this - replace YOURSERVERFQN with your server domain

upstream gitlab-workhorse {
  server unix:/var/opt/gitlab/gitlab-workhorse/socket fail_timeout=0;
}


server {

  listen 0.0.0.0:80;

  server_name YOUR_SERVER_FQN;
  server_tokens off;

  location / {
    return 301 https://$http_host$request_uri;    
  }

  # Letsencrypt Verification
  #
  location ~ /.well-known {
    root /usr/share/nginx/html;
    allow all;
  } 

  access_log  /var/log/nginx/gitlab_access.log;
  error_log   /var/log/nginx/gitlab_error.log;

}


server {

  listen 0.0.0.0:443 ssl;

  server_name YOUR_SERVER_FQDN;
  server_tokens off;

  root /opt/gitlab/embedded/service/gitlab-rails/public; 

  ssl on;
  ssl_certificate /etc/letsencrypt/live/git.YOUR_SERVER_FQN/fullchain.pem;
  ssl_certificate_key /etc/letsencrypt/live/git.YOUR_SERVER_FQN/privkey.pem;

  ssl_protocols TLSv1 TLSv1.1 TLSv1.2;

  ssl_prefer_server_ciphers on;
  ssl_ciphers "ECDHE-RSA-AES256-GCM-SHA384:ECDHE-RSA-AES128-GCM-SHA256:ECDHE-RSA-AES256-SHA384:ECDHE-RSA-AES128-SHA256:ECDHE-RSA-AES256-SHA:ECDHE-RSA-AES128-SHA:ECDHE-RSA-DES-CBC3-SHA:AES256-GCM-SHA384:AES128-GCM-SHA256:AES256-SHA256:AES128-SHA256:AES256-SHA:AES128-SHA:DES-CBC3-SHA:!aNULL:!eNULL:!EXPORT:!DES:!MD5:!PSK:!RC4";
  ssl_ecdh_curve secp384r1;

  ssl_session_cache shared:SSL:10m;
  ssl_session_tickets off;

  ssl_stapling on;
  ssl_stapling_verify on;

  resolver 8.8.8.8 8.8.4.4 valid=300s;
  resolver_timeout 5s;

  add_header Strict-Transport-Security "max-age=63072000; includeSubdomains";
  add_header X-Frame-Options DENY;
  add_header X-Content-Type-Options nosniff;

  ssl_dhparam /etc/ssl/certs/dhparam.pem;  

  access_log  /var/log/nginx/gitlab_access.log;
  error_log   /var/log/nginx/gitlab_error.log;

  location / {
    client_max_body_size 0;
    gzip off;

    proxy_read_timeout      300;
    proxy_connect_timeout   300;
    proxy_redirect          off;

    proxy_http_version 1.1;

    proxy_set_header    Host                $http_host;
    proxy_set_header    X-Real-IP           $remote_addr;
    proxy_set_header    X-Forwarded-Ssl     on;
    proxy_set_header    X-Forwarded-For     $proxy_add_x_forwarded_for;
    proxy_set_header    X-Forwarded-Proto   $scheme;
    proxy_pass http://gitlab-workhorse;
  }

}

I have the same problem, But still can't fix it.
Are there any idea.
Please help us. :(