The intensity correlation time T is studied by employing a gain-noise model of a single-mode laser driven by coloured pump noise τ1 and coloured quantum noise τ2 with coloured cross-correlation τ3 with a bias signal modulation. By using the linear approximation method, we detect that a maximum (i.e. resonance) exists in the curves of the intensity correlation time T versus the noise intensities D and Q when the noise correlation coefficient λ is positive; and a minimum (i.e. suppression) exists in the T-D and T - Q curves when λ is negative.When λ is zero, T increases monotonously with increase of D and decreases monotonically with increase of Q.Furthermore, the curve of T versus the pump noise self-correlation time τ1 is also studied. Our study shows that,no matter what the value of λ is, there exist one maximum and one minimum in the T - τ1 curve.