In this paper, the multicell distributed beamforming (MDBF) design problem of suppressing intra-cell interference (InCI) and inter-cell interference (ICI) is studied. To start with, in order to decrease the InCI and ICI caused by a user, we propose a gradient-iteration altruistic algorithm to derive the beamforming vectors. The convergence of the proposed iterative algorithm is proved. Second, a metric function is established to restrict the ICI and maximize cell rate. This function depends on only local channel state information (CSI) and does not need additional CSIs. Moreover, an MDBF algorithm with the metric function is proposed. This proposed algorithm utilizes gradient iteration to maximize the metric function to improve sum rate of the cell. Finally, simulation results demonstrate that the proposed algorithm can achieve higher cell rates while offering more advantages to suppress InCI and ICI than the traditional ones.