We have investigated the Mn2PtAl Heulser alloy to unravel its structural, magnetic, calorimetric and electronic structure properties. At room temperature, the alloy crystallizes in a hexagonal structure. Magnetization reveals a weak martensitic transition at 307 K, followed by a long range ferrimagnetic transition at 90 K. Griffiths phase-like signature and positive Weiss temperature in dc-magnetization, isothermal magnetic hysteresis loops and a frequency-independent peak confirm a nearly compensated ferrimagnetic order of Mn2PtAl. The theoretical electronic structure calculations also reveal the ferrimagnetic ground state of Mn2PtAl and Mn ions (occupying different sites) with a very small total magnetic moment. A giant exchange bias field of 2.73 kOe, at a temperature of 3 K and a cooling field of 70 kOe, has been estimated and is attributed to the unidirectional anisotropy associated with possible ferromagnetic clusters formed by the field cooling process in the ferrimagnetic matrix.