The effects of multiple time delays on an intracellular calcium oscillation (ICO) system with correlated noises were investigated by means of stochastic simulation. Suppose the pumping of Ca^2+ into the calcium store takes time τ1, and the release of Ca^2+ from that store into the cytosol takes time τ2. The simulation results indicate that: (i) There is a critical value τc ≃ 0.1 s of τ1, i.e., as τ1 < τc, increasing τ1 can restrain ICO and convert the structure of the stationary probability distribution (SPD) of the intracellular Ca^2+ concentrations from two peaks to one peak. However, in contrast, if τ1 > τc, increasing τ1 can convert the SPD to the opposite and change the Ca^2+ concentrations from desynchronous oscillation to periodically synchronous oscillation; (ii) Increasing τ2 converts the SPD from two peaks to one peak and restrains ICO; (iii) As τ2 increases a coherence resonance with respect to τ1 occurs in the system, but it is inhibited by increasing the external noise.