Magnetoelectric (ME) effect has given rise to a new design principle for novel low-power electronic devices. The polar magnet ${\mathrm{Fe}}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ with linear ME effect is one of the promising candidates. Unfortunately, for this material, a large ME response only appears in the ferrimagnetic state, which needs a high magnetic field to be activated. In this work, we successfully synthesize single-crystal ${({\mathrm{Fe}}_{0.95}{\mathrm{Mg}}_{0.05})}_{2}{\mathrm{Mo}}_{3}{\mathrm{O}}_{8}$ (FMMO), which achieves a linear ME effect in the antiferromagnetic ground state and shows a significantly improved ME coefficient in the ferrimagnetic state. Compared with the parent phase, six times linear ME coefficient and more than ten orders of magnitude second-order ME coefficient are accomplished in the FMMO. The spin-lattice coupling and the exchange-striction mechanism are believed to play a crucial role in creating the giant ME effect. The present study provides an idea for designing materials with strong ME coupling.