By adopting the gain-noise model of the single-mode laser in which with bias and periodical signals serve as inputs, combining with the effect of coloured pump noise, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio (SNR) of the laser intensity under the condition of pump noise and quantum noise cross-related in the form of 'delta' function. It is found that with the change of pump noise correlation time, both SNR and the output power will occur stochastic resonance (SR). If the bias signal 'alpha' is very small, changing the intensities of pump noise and quantum noise respectively does not lead to the appearance of SR in the SNR; while 'alpha' increases to a certain number, SR appears.