I have a question, hope someone here can give me answer. Thank you.

The question is: when you adopt FVM to solve governing eq. the governing eq. should be in a conservation form. Namely, for the governing eq. which is in non-conservation form, FVM method can not be employed, am I right?

Not exactly. Mathematically you can integrate any equation with volume. For example volume intergral (a*grad(b)) can be approximated as A *volume intergral(grad(b)) where you have to get A from some sort of average of a. For fluid flow, you have mass conservation equation, momentum conservation equation, energy and species conservation equation: these equations are inherently in a conservation form unless otherwise manipulated.