We theoretically investigate a possibility of improving the thermoelectric performance of monolayer InSe through convergence of multivalley energy bands, in which some distinct valleys become almost degenerate. The convergence of energy bands is achieved by applying mechanical strain. We find that the thermoelectric power factor of monolayer InSe can be significantly enhanced by nearly a factor of 3 through the band convergence in both valence (p-type) and conduction (n-type) bands under a biaxial compressive stress of about 1.16 GPa. However, the maximum enhancement of the figure of merit Z T in the p-type and n-type InSe differs each other depending on how the valleys converge in each case. The optimal scenario is that the heavy valleys approach the light valleys in the band convergence, which leads to an increase in the power factor and, at the same time, a decrease in the thermal conductivity of an electron. This optimal condition can be obtained in the strained n-type InSe that gives the largest enhancement of Z T as high as 230% Z T of unstrained InSe. In contrast, the enhancement of Z T in the strained p-type InSe, which exhibits opposite valley convergence (light valleys joining heavy ones), gives only 26% Z T of unstrained InSe.