Wet joints are widely used in precast steel–concrete composite bridges to accelerate the construction of bridges, though a conventional wet joint usually has a poor ultimate shear capacity. To improve the shear capacity of the wet joint, a concave square frustum-shaped wet joint was proposed, and the failure modes and ultimate shear capacity were studied experimentally and numerically. Specimens with concave square frustum-shaped and conventional wet joints (labeled as S-SWJ and S-CWJ) were fabricated, and experiments were performed on them. The results showed that the ultimate shear capacity of S-SWJ was substantially enhanced compared to that of S-CWJ. To further explore the ultimate shear capacity of S-SWJ, the failure modes and the influences of concrete strength and shear key angle on the ultimate shear capacity were studied using a validated finite element (FE) model. Based on the FE analysis, the guidelines for obtaining a wet joint with desirable shear capacity are presented, which is useful for the design of wet joints with high ultimate shear capacity.