In the present work, two successive magneto-structural transformations (MSTs) consisting of martensitic and intermartensitic transitions have been observed in polycrystalline Ni_55.8Mn_18.1Ga_26.1 Heusler alloy. Benefiting from the additional latent heat contributed from intermediate phase, this alloy exhibits a large transition entropy change ΔS_tr with the value of ~27 J/kg K. Moreover, the magnetocaloric effect (MCE) has been also evaluated in terms of Maxwell relation. For a magnetic field change of 30 kOe, it was found that the calculated value of refrigeration capacity in Ni_55.8Mn_18.1Ga_26.1 attains to ~72 J/kg around room temperature, which significantly surpasses those obtained for many Ni-Mn based Heusler alloys in the same condition. Such an enhanced MCE can be ascribed to the fact that the isothermal entropy change ΔS_T is spread over a relatively wide temperature interval owing to existence of two successive MSTs for studied sample.