DeltaG for phase transition could be easily calcuIated using commercial thermodynamic package, e.g. FactSage, providing that thermodynamic data is available.

What kind of material is it? Organic, metallic, ceramic?

DSC is a very common experimental method to measure the enthalpy, melting point and heat capacity differences between phases. It is then possible to calculate the Gibbs free energy difference using standard thermodynamic expressions. Li Yuan has developed such methods for organic molecular polymorphs. I'm not sure how to apply such methods to inorganic materials.

In principle it is also possible to calculate the free energy difference by density functional theory and lattice dynamics if you know the atomic structures of the two phases.

Thank you Qifeng and Jonas

My material is inorganic.

Are there any other experimental methods other than DSC.

Mr. Jonas could you give me any references for calculating it by DFT.

I would probably try this:

https://arxiv.org/pdf/1410.8231.pdf

You will need a density functional program too, Quantum Espresso is suitable and free to use. Note that calculations like these require considerable expertise if you want results are are comparable to experiments.