An intracellular calcium oscillations model subject to external colored noise is investigated. Internal signal stochastic resonance (ISSR) can be induced and significantly influenced by colored noise. The signal-to-noise ratio (SNR) exhibits two maxima with the increment of the correlation time as the noise intensity is fixed, indicating the occurrence of stochastic bi-resonance. Additionally, we find ISSR and explicit internal signal stochastic resonance (EISSR) have quite similar responses to colored noise, which implies there are some commonalities in their mechanisms.