In this paper,two time-domain explicit expressions of the non-stationary random seismic response sensi- tivity are derived respectively based on the precise integration format and the Newmark-β integral format,and they are respectively used to analyze the sensitivity of a plane frame and a plane truss structure.Then,the effects of the integral time step on the calculation accuracy and the efficiency of the two integral formats are investigated.It is found that,when the main frequency of the structure is within the range of the main load frequency,the time-do- main explicit expression based on the precise integration has a higher efficiency with the same accuracy,but when the main frequency of the structure deviates from the main load frequency range,the time-domain explicit expres- sion based on the Newmark-β integral format achieves a higher efficiency.The research achievements can provide an effective reference for the choice of the numerical integration algorithms used in the structure optimization consi- dering the non-stationary random vibration.