Abstract Previous studies have shown that the dependence of the pulse temporal properties (pulse width, pulse rise width, pulse decay width, and pulse peak time) on energy is a power-law function. In this work we demonstrate that the power-law indices of the pulse width, pulse rise width, pulse decay width, and pulse peak time on energy are correlated with the spectral lag and the relative spectral lag, $ \bigtriangleup t_{31}/w_{3}$ (where $ \bigtriangleup t_{31}$ and $ w_{3}$ are the spectral lag between BATSE channels 1 and 3 and the pulse width of BATSE channel 3, respectively), using a sample including 102 well-separated long-duration gamma-ray burst pulses. In addition, the correlations of the power-law indices with the relative spectral lags are much more tighter than those with the spectral lags. We further find that the power-law indices are also correlated with the pulse photon flux. The possible origins of these correlations are also discussed. We argue that the kinematic effect can explain the correlated properties.