Ca

2+

is the most commonly used signal that appears as sustained oscillations to regulate many diverse cellular processes. Two-pool model is a classical mathematical model to explain how these Ca

2+

oscillations occur. However

the Hill coefficient in this model is too high to do mathematical analysis. In this paper

we improve the original model by lower the Hill coefficient. Based on the qualitative theory and bifurcation theory

we analyze the existence and stability of equilibrium points

and discuss the type of bifurcation points in the improved model. The improved model has similar dynamic properties as the original model

but a wider region for Ca

2+

oscillations and a more obvious amplitude change

which better reflects the information encoding role of Ca

2+

signaling. The results of two-parameter bifurcation analysis combined with parameter sensitivity analysis indicate that the efflux rate constant of Ca

2+

out of the cell

as well as the threshold constants for activation and pumping of Ca

2+

store have significant impact on Ca

2+

oscillations. The variation of these parameters may contribute to calcium-related disease. This research is not only helpful for studying the two-pool model from the mathematical aspect

but also for understanding the Ca

2+

signaling and related diseases.