Superconductivity is one of the most intriguing topics in solid state physics. Generally, the superconducting Cooper pairs are broken by the Zeeman effect, which gives the so-called Pauli paramagnetic limit H_Pauli. However, when the superconductivity is in the clean limit and the orbital effect is strongly quenched, the Cooper pairs can survive even above H_Pauli, which is the so-called Fulde and Ferrell, and Larkin and Ovchinnikov (FFLO) phase. Extensive efforts have been devoted to the discovery of the FFLO phase. However, vortex phase transitions have given rise to considerable ambiguity in the interpretation of the experimental data. Here, we report comprehensive magnetocaloric and torque studies of the FFLO phase transition in a highly two-dimensional organic superconductor. We observe the FFLO phase transition clearly distinct from vortex melting transitions. The phase diagram provides crucial information on the stability of the FFLO phase in magnetic fields.