"I would like to turn on the street lights for 3 hours and off for 2 hours by using contactor and timer. That lights design on solar system. Kindly help me out how to make the logic and get desired output.

Are you referring to street lights on the curb that are maintained by your local government or lights you installed?

A correctly sized 12 Volt timer maybe, or a good 120 Volt timer and a relay, all depending on your voltage and load.

We installed that lights... we want to turn on that for 3 hours. Kindly help me and draw line diagram

A correctly sized 12 Volt timer maybe, or a good 120 Volt timer and a relay, all depending on your voltage and load.

Please give me line diagram by using timer and contactor .

I cannot provide you with a schematic. You have to design your system based on the operating voltage and the load of the lights.
If you can find a timer that will run (power to the timer clock) on the same voltage as the voltage for the lights- you can use just a timer.
If the voltage required for the timer clock is not the same as the voltage on which the lights operate, you need to find a timer that will operate for instance on your household power, then have that timer operate a relay that is capable of carrying the amperage drawn by the lights.

Here are some timers:

https://www.google.com/search?q=timer+for+solar+power&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a#q=timer+for+solar+power&rls=org.mozilla:en-US:official&tbm=shop

I just need a idea.. how can I made this circuit, I used breaker timer and contactor for testing. But I can't found the desired output.

How many lights? What is the voltage and wattage of the lights?
Can you give us a description of your system?
Are you using a timer similar to this one?
Intermatic ML88T - 88 Watt - Transformer with Timer (http://www.1000bulbs.com/product/85588/ELEC-ML88T.html?utm_source=SmartFeedGoogleBase&utm_medium=Shopping&utm_term=ELEC-ML88T&utm_content=Transformers&utm_campaign=SmartFeedGoogleBaseShopping&gclid=CNq8k_iTgLoCFcOj4AodBAoADg)

60 lights... each light 100 watt..
All are street lights.. . system run on solar

Similar to these?
http://mysunlight.co.in/images/solar_street_light.gif

Could you use photocells, automatic on/off. What is the basis for wanting 3 hours on and only 2 hours off?
Is this a municipal system? Where?

It's a housing society.. pv cells is not automatic.

Find a timer that will operate on the electrical system for your area.
Have the timer (at the times you desire) provide power to a relay designed to operate at the same voltage the timer is powered by, and the relay being capable of carrying the voltage and amperage of the lighting load. The power to the relay will close the contacts in the relay and the lights will be on and when the timer shuts off power to the relay, the lights will go off.
How Relays Work | Relay diagrams, relay definitions and relay types (http://www.galco.com/comp/prod/relay.htm)
Or, find a timer (or timers if load is too great for one timer) that operates on the voltage produced by the solar circuit, set the on/off times and hook the lights to the terminals on the timer that are powered when the timer reaches the on-time.
Good luck with your project.