Femtosecond lasers have evolved continuously over the past three decades, enabling the transition of research from fundamental studies in atomic and molecular physics to the realm of practical applications. In femtosecond laser amplifiers, to ensure strict synchronization between the seed laser pulse and the pump laser, enabling their precise overlap during the amplification process and avoiding a decline in pulse amplification efficiency and the generation of undesired phase noise, this study designed a synchronous timing signal generation system based on the combination of FPGA and analog delay. This system was investigated from three aspects: delay pulse width adjustment within a certain range, precise delay resolution, and external trigger jitter compensation. By using a FPGA digital counter to achieve coarse-delay control over a wide range and combining it with the method of passive precise fine delay, the system can generate synchronous delay signals with a large delay range, high precision, and multiple channels. Regarding the problem of asynchronous phase between the external trigger and the internal clock, a jitter compensation circuit was proposed, consisting of an active gated integrator and an output comparator, which compensates for the uncertainty of trigger timing through analog delay. The verification of this study shows that the system operates stably under an external trigger with a repetition frequency of 80 MHz. The output delay range is from 10 ns to 100 $\mu$s, the coarse-delay resolution is 10 ns, the fine-delay adjustment step is 1.25 ns, and the pulse jitter is reduced from a maximum of 10 ns to the hundred-picosecond level. This meets the requirements of femtosecond laser amplifiers for synchronous trigger signals and offers essential technical support and fundamental assurance for the high-power and high-efficiency amplification of Ti:sapphire ultrashort laser pulses.