I have two routers connected to each other. Both the routers are connected to the WAN using two different ISPs.
Router A is used for the day to day browsing in the office while Router B is connected to a web server that serves pages to public.
When someone from Router A wants to access our website from Router B, the connection is getting through the WAN. I want to redirect that particular through the LAN instead. Is there any way to do it using the Router A (D-Link DIR-655)?
To summarise, if people in the office want to access pages from 60.51.223.223 (WAN of Router B), the traffic should go through Router B, which resolves the request locally. Router B is a client under Router A.
This is the network map:
Network diagram http://www.nirmalnatarajan.com/images/networkMap.png
As justinsteven noted, you can use DNS or local hosts files to direct the web site traffic to the internal IP address. Then set a route on each router for the other internal network, and all will work. If the two routers are "consumer grade" this might not be possible.
However ...
This configuration is not very secure, and would be keeping me awake at night. There is no real firewall, the web server is publicly accessible and has unfettered access to the rest of the network. The possibility of routing loops and performance problems is very real. I would take the cable connecting the internal networks out immediately. Sending that traffic through the internet is wise, since you don't have a properly configured network.
A far better solution is to get a good firewall (I like Astaro), plug both ISP connections into it as well as both internal networks, and configure it. Astaro offers a basic version of the software for free, so you can put 4 NICs into an older PC and away you go.
Add a route on Router A that uses Router B as the gateway for the networks which Router B serves. (Make sure that Router B has a route back to Router A.)
If this doesn't solve your problem, I highly suggest you reword your question - a network diagram should help.
Have a look at the Advanced\Routing tab.
In your example, you'd have something like this:
Name: Whatever
Destination IP: 60.51.223.223
Netmask: 255.255.255.255
Gateway: IP Address of the other router (B)
For further information have a look at the help page.
It's not the cleanest solution, but if you have an internal name server, you could add an A record for the website's name and give it the internal server address. If you're only talking about a handful of internal machines, you could do this on each via the hosts file.