Hi I have read that implicit methods should not be used with unstaedy problems. Explicit method is best suited for unsteady problems. Can anybody suggest reason.

Implicit methods can be used for unsteady flows. Many years ago most implicit methods were constructed using forms of the equations that did not treat the transient terms correctly. Hence those schemes were not suitable for unsteady simulations. But as long as the transient term is treated properly and the time step used is sufficient to resolve the time scales of interest, implicit methods can be used for unsteady flows. Whether they are the most efficient is another question and depends on the time scales you are trying to resolve (among other things).

Not only are implicit methods often suitable, as ag said, but they are actually quite frequently the method of choice, with one exception: Explicit methods are superior if accuracy considerations demand such a small time-step that the stability issues of the explicit method (and the advantage of the implicit approach) become irrelevant. This clearly depends on the application (and scheme). What is your application?

but when you will have small time step, then can it work? I mean which will be better at that time, explicit or implicit? i.e., When u have very small time step then which will be better?

It is reallly a question of efficiency - if your time step must be so small as to satisfy a CFL constraint, then explicit methods will generally be the correct choice. The reason for this is that explicit codes typically run much faster than implicit codes. However, understand that "small time step" is a meaningless term if you don't state how you define "small". In many cases a "small" time step that is appropriate for the simulation physics is still much larger than any CFL criterion. In such a case an implicit method would be a better choice.