We report on an experimental and theoretical study of a large-aperture Ti:Sapphire (Ti:S) amplifier pumped with a novel temporal dual-pulse scheme to suppress the parasitic lasing (PL) and transverse amplified spontaneous emission (TASE) for high-energy chirped-pulse amplification (CPA). The pump energy distribution was optimized and the time delay between each pump pulse was controlled precisely. Both the numerical and experimental results confirm that the temporal dual-pulse pump technique can effectively suppress PL and TASE. The maximum output energy of 202.8 J was obtained from the final 150-mm-diameter Ti:S booster amplifier with a pump energy of 320.0 J, corresponding to a conversion efficiency of 49.3%. The compressed pulse duration of 24.0 fs was measured with a throughput efficiency of 64%, leading to a peak power of 5.4 PW. This novel temporal dual-pulse pump technique has potential applications in a 10 PW CPA laser system.