Multiple input multiple output (MIMO) relay channels has great application potentials in wireless communication systems and therefore attracts both academia and industrial attentions recently. In this paper, we consider the MIMO relay channels where both source node and relay node are equipped with multiple antennas and the destination node has a single antenna. We address the optimal beamforming design when decode-and-forward half-duplex relaying protocol is deployed. Specifically, we develop an efficient algorithm to determine the optimal beamforming vector at the source when transmitting to relay and destination at the same time. Based on the exact channel capacity formulation, the proposed algorithm can achieve arbitrarily high accuracy with low computational complexity.