The crystal structures, martensitic structural transitions and magnetic properties of MnCo1-xFexSi (0 <= x <= 0.50) alloys were studied by differential scanning calorimetry (DSC), x-ray powder diffraction (XRD) and magnetic measurements. In high-temperature paramagnetic state, the alloys undergo a martensitic structural transitions from the Ni2In-type hexagonal parent phase to the TiNiSi-type orthorhombic martensite. Both the martensitic transition temperature (TM) and Curie temperatures of martensite (T_C^M) decrease with increasing Fe content. The introduced Fe atoms establish ferromagnetic (FM) coupling between Fe-Mn atoms and destroy the double spiral antiferromagnetic (AFM) coupling in MnCoSi compound, resulting in a magnetic change in the martensite phase from a spiral AFM state to a FM state. For the alloys with x = 0.10, 0.15 and 0.20, a metamagnetic transition was observed in between the two magnetic states. A magnetostructural phase diagram of MnCo1-xFexSi (0 <= x <= 0.50) alloys was proposed.