In this study we have performed DFT based calculations on lead-free Na2MoXO6 (X = Si, Ge, and Sn) double perovskites (DPs) for photovoltaic and optoelectronic applications. Trans-Blaha modified Becke-Johnson potential (TB-mBJ) approximation is used to calculate electronic properties of the given materials. All the given perovskites are found in cubic symmetry exhibiting semiconducting nature with energy band gap ∼1.77 eV, 1.65 eV and 1.33 eV, respectively. The calculated values of tolerance factor τ and negative formation energy demonstrate the structural and thermodynamic stabilities of all the investigated compounds. The elastic study demonstrates the ductile and anisotropic nature of Na2MoXO6 (X = Si, Ge, and Sn) compounds. In addition Na2MoXO6 (X = Ge, and Sn) compounds exhibit large absorption coefficient in visible light among the investigated perovskites. Overall the study demonstrates the suitability of investigated compounds for solar cell and other optoelectronic devices because of their narrow band gap and absorption performance.