After I type in my browser www.site2.com, it open page of www.site1.com.
I think my configuration for both nginx and gunicorn are fine.

etc/nginx/site-available/site1 - my default website www.site1.com

upstream app_server {
    server 127.0.0.1:9000 fail_timeout=0;
}

server {
    listen 80 default_server;
    listen [::]:80 default_server ipv6only=on;

    root /usr/share/nginx/html;
    index index.html index.htm;

    client_max_body_size 4G;
    server_name _;

    keepalive_timeout 5;

    # Your Django project's media files - amend as required
    location /media  {
        alias /home/django/site1/media;
    }

    # your Django project's static files - amend as required
    location /static {
        alias /home/django/site1/static_root;
    }

    location / {
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_pass http://app_server;
    }
}

etc/nginx/site-available/site2 - my new website www.site2.com

upstream app_server2 {
    server 127.0.0.1:9500 fail_timeout=0;
}

server {
    listen 80;
    listen [::]:80;

    root /usr/share/nginx/html;
    index index.html index.htm;

    client_max_body_size 4G;
    server_name www.site2.com site2.com;

    keepalive_timeout 5;

    # Your Django project's media files - amend as required
    location /media  {
        alias /home/django/test-django/site2/media;
    }

    # your Django project's static files - amend as required
    location /static {
        alias /home/django/test-django/site2/static;
    }

    location / {
        proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
        proxy_set_header Host $http_host;
        proxy_redirect off;
        proxy_pass http://app_server2;
    }
}

etc/init/site1.conf

description "Gunicorn daemon for Django project"

start on (local-filesystems and net-device-up IFACE=eth0)
stop on runlevel [!12345]

# If the process quits unexpectedly trigger a respawn
respawn

setuid django
setgid django
chdir /home/django

exec gunicorn \
    --name=site1\
    --pythonpath=site1 \
    --bind=0.0.0.0:9000 \
    --config /etc/gunicorn.d/gunicorn.py \
    site1.wsgi:application

etc/init/site2.conf

description "Gunicorn daemon for Django project"

start on (local-filesystems and net-device-up IFACE=eth0)
stop on runlevel [!12345]

# If the process quits unexpectedly trigger a respawn
respawn

setuid django
setgid django
chdir /home/django/test-django/

exec gunicorn \
    --name=site2\
    --pythonpath=site2 \
    --bind=127.0.0.1:9500 \
    --config /etc/gunicorn.d/gunicorn.py \
    site2.wsgi:application

I didn’t forget about sudo service nginx restart and service site2 restart, also after nginx -t I don’t have any erros.