To practically predict the design criteria of diode-end-pumped passively Q-switched (PQS) lasers with energy scaling to millijoule region, an analytical model with longitudinally spatial dependence is derived to investigate the influence of pump beam quality. In comparison with PQS theory that considers transverse spatial dependence only, it is found that the threshold pump power can be up to 5 times larger when the beam quality factor was 80. This result indicates the importance of considering pump beam quality when designing PQS lasers especially for operation at high pump power level. The theoretical results are verified by a series of PQS experiments. The influence of thermal lensing effect on cavity design is further discussed to obtain good laser quality. Finally, an end-pumped millijoule PQS laser is successfully realized based on the theoretical analysis and the resonator design.