Complete complementary sequence (CCS) design has become an important topic in recent years due to its theoretically ideal zero sidelobe performance. However, the main obstacle for the widespread use of the CCS is its sensitivity to the Doppler shift. In this letter, a method for constructing the CCS with the desired matrix-valued ambiguity functions under a peak-to-average-power ratio (PAR) and an energy constraint is proposed. A gradient-based nonlinear iterative algorithm is used to solve the constrained sequence design problem. Numerical results are presented to show that, compared with the state-of-the-art methods, the proposed method can produce CCS with better correlation properties and the Doppler tolerance. Finally, indoor experiments are conducted to verify the superior performance of the designed CCS, and a peak sidelobe level under −45 dB is realized on the hardware system.