Using first-principles density-functional theory, we investigate systematically the structural, magnetic, and mechanical properties of In2(Mo,W)X (X = Cr, Mn, Fe, Co, and Ni) Heusler alloys. All the studied compounds have a regular structure with different magnetic configurations. By calculating the total energy of a martensitic phase with respect to the austenitic phase, a number of new In2-based magnetic shape memory alloys, In2(Mo,W)X (X = Cr, Mn, Fe, and Co), are first predicted to emerge with the tetragonal martensite phase as their ground state. The tetragonal shear modulus and elastic anisotropy ratio of In2(Mo,W)X (X = Cr, Mn, Fe, and Co) alloys also satisfy the criterion of the martensitic phase. Interestingly, all the In2(Mo,W)X (X = Cr, Mn, Fe, and Co) alloys exhibit higher martensitic start temperature and better ductility in comparison with the well-known material Ni2MnGa.