A triple-layer transmitarray consisting of unit cells with limited phase range is studied in this letter. A 255° phase shift with high transmission (better than $-\hbox{1 dB}$) is achieved by the proposed split diagonal cross element. This limitation of phase range makes the commonly used ray-tracing method unable to solve the required phase shift distribution and maintain high transmission simultaneously. A global search method, namely the particle swarm optimization, is applied to address the constrained phase only synthesis problem. The results suggest that the backward radiation is suppressed by 9.2 dB and the sidelobe by 4.1 dB compared to the ray-tracing method. A prototype has been manufactured and tested. The measured performance shows a good agreement with the simulation by a gain level of 18.9 dBi and a 1-dB bandwidth of 9.6%.