Mutually orthogonal periodic complementary sequence sets (MOPCSS) and their application are investigated in this letter. A new generator for quadriphase MOPCSSs is first presented, which uses a unitary-like matrix as a seed matrix. Next, a new design of pilot sequences using MOPCSSs for multiple-input and multiple-output (MIMO) single-carrier block transmission (SCBT) systems is given. Later on, an optimized periodic Golay correlator is proposed to efficiently implement the least square MIMO channel estimation. Finally, the optimal performance of the channel estimation is verified via simulation.