Double-perovskite A2BB'O6 oxides with magnetic B and B' ions and E*-type antiferromagnetic order (E*-AFM, i.e. the ↑↑↓↓ structure) are believed to exhibit promising multiferroic properties, and Y2CoMnO6 (YCMO) is one candidate in this category. However, the microscopic origins for magnetically induced ferroelectricity in YCMO remain unclear. In this study, we perform detailed symmetry analysis on the exchange striction effect and lattice distortion, plus the first-principles calculations on YCMO. The E*-AFM state as the ground state with other competing states such as ferromagnetic and A-antiferromagnetic orders is confirmed. It is observed that the ferroelectricity is generated by the exchange striction associated with the E*-AFM order and chemically ordered Mn/Co occupation. Both the lattice symmetry consideration and first-principles calculations predict that the electric polarization aligns along the b-axis. The calculated polarization reaches up to 0.4682 μC cm(-2), mainly from the ionic displacement contribution. The present study presents a comprehensive understanding of the multiferroic mechanisms in YCMO and is of general significance for predicting emergent multiferroicity in other double-perovskite magnetic oxides.