One approach to support floating tidal current turbines is by using a moored catamaran, a barge type platform. Considering its low draft, one might expect that it performs best at typical straits with sea states of small wavelets to small waves. The problem is that the high rotational motion responses of the catamaran due to wave loads tend to reduce the turbine performance. This paper looks for a possibility to deteriorate these rotational responses by introducing a platform with four buoyant legs referred to as a quad-spar considering its good stability performance. The platforms are moored by four catenary cables as their mooring system. The motion response modeling was undertaken by Computational Fluid Dynamic (CFD) simulation based on three-dimensional potential flow theory. Considering sea states of straits with typical tidal current energy potentials, the environmental load was set on random wave with the significant wave height, Hs, of about 0.09 to 1.5 m and the wave period, T, of about 1.5 to 6 s corresponding to the wave frequency, ω, of about 1.1 to 4.2 rad/s. This study found that lower motion responses can be satisfied by the quad-spar, in which its yaw, roll and pitch responses are on average about 5%, 44%, and 38%, respectively, compared to those of the catamaran. This result indicates that the quad-spar is more effective in reducing rotational motion responses needed to keep a high performance of the tidal current energy system.