A laser diode (LD) dual-end pumped, conductively cooled, electro-optical Q-switched composite Nd:YAG laser is designed. Double-pulse laser output with adjustable pulse interval is achieved. By using two fiber-coupled LD modules as the pumping source, β-BaB2O4 (BBO) crystal as the Q-switch, double-pulse laser output is acquired by opening the Q-switch twice in a pumping cycle time, and the laser is capable of producing two Q-switched 1064 nm pulses with the single pulse energy more than 14 mJ, 18 ns, the interval between the two pulses is adjustable from 200 s to 230 s at the repetition of 50 Hz, the optical-to-optical efficiency reaches 24%. Furthermore, we explore the feasibility of stable double-pulse laser output by using the Q-switched crystal KD2PO4 (KD*P), and suppressing the piezoelectric ring effect of KD*P, the sub-pulse phenomenon is removed and double-pulse laser output with 11 mJ, 18 ns, is obtained.