Collaborative transmission among evolved Node-Bs (eNBs) is one of the promising techniques for LTE-Advanced to provide broader coverage and higher spectral efficiency. The interference among multi-cell transmission can be mitigated by joint precoding, such as multi-cell block diagonalization (BD) at cooperative eNBs. The major difference between multi-cell and single-cell transmission is that the power constraint has to be considered on a per-eNB basis. To satisfy per-eNB power constraint (PePC), a simplified power allocation algorithm for the multi-cell BD based collaborative transmission is proposed in this paper. The algorithm provides a power allocation coefficient matrix for BD to meet PePC. Simulation results demonstrate that the proposed algorithm has a near-optimal performance with simplicity.