This doc is based on facebook login in web2py doc:

https://github.com/web2py/web2py/blob/master/gluon/contrib/login_methods/oauth20_account.py

1. First of all you will need to get from linkedin the key and secret.
2. Install python-linkedin lib: pip install python-linkedin

In the module folder create a new python file, for example linkedin.py:

from gluon.http import HTTP
try:
    from linkedin.linkedin import LinkedInApplication
except ImportError:
    raise HTTP(400, "linkedin module not found")
from gluon.contrib.login_methods.oauth20_account import OAuthAccount
import hashlib
import random

LK_KEY = ''
LK_SECRET = ''
LK_RETURN_URL = 'http://localhost:8000/socialSignIn/default/index'

class LinkedInAccount(OAuthAccount):
    TOKEN_URL="https://www.linkedin.com/uas/oauth2/accessToken"
    AUTH_URL="https://www.linkedin.com/uas/oauth2/authorization"

    def __init__(self):
        OAuthAccount.__init__(self, 'linkedin', LK_KEY, LK_SECRET,
                              self.AUTH_URL, self.TOKEN_URL,
                              scope='r_emailaddress',
                              state=self._make_new_state())

    def _make_new_state(self):
        return hashlib.md5(
            '%s%s' % (random.randrange(0, 2 ** 63), LK_SECRET)).hexdigest()

    def get_user(self):
        if not self.accessToken():
            return None
        app = LinkedInApplication(token=self.accessToken())
        profile = app.get_profile(selectors=['id', 'first-name', 'last-name', 'email-address'])
        if profile:
            if not profile.has_key('username'):
                username = profile['id']
            else:
                username = profile['username']

            if not profile.has_key('emailAddress'):
                email = '%s.fakemail' %(profile['id'])
            else:
                email = profile['emailAddress']

            return dict(first_name = profile['firstName'],
                            last_name = profile['lastName'],
                            username = username,
                            email = '%s' %(email) )

In your model db.py:

from linkedin import LinkedInAccount
auth.settings.login_form=LinkedInAccount()