The evolution of the dynamic behaviors of beating rhythms from independent states to the formation of network is studied in biological experiment on two heterogeneous cells. The beating rhythms are independent and not synchronous when there is no coupling between two cells. With the enhancement of the coupling strength, the mean and maximum of absolute value of the phase difference drastically decrease in the beating rhythms of the two cells, from non-phase synchronization to phase synchronization, eventually not to full synchronization. Some of beatings become synchronous while others not synchronous for non-synchronization states while all beatings are synchronous for the phase synchronization state. With the increase of coupling strength, the times of synchronized beatings increases for the non-phase synchronization state, and time interval between the corresponding synchronous beatings of the two cells decreases to a low but non-zero value for the phase synchronization state. The results not only provide experimental demonstration of rhythm synchronization in a biological network, but also give changing regularity in the forming process of synchronous rhythm in the heterogeneous network.