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In order to improve the real-time performance of inverse kinematics for 6R robots, a real-time and efficient algorithm based on vector dot product was proposed. The complex matrix equations were transformed to 10 pure algebraic equations containing 6 unknown joint variables, and symbolic preprocessing was applied in simplifying equations without any error accumulations caused by floating-point calculations. The production of extraneous roots in the solving process of the 5th and 6th joint variables was avoided by optimizing the linear combinations of related equations, which greatly improved the efficiency of the algorithm. Experiments on a 6R robot show that, the proposed algorithm has a stronger real-time performance than those of others to get the same precision solutions, the average time for gaining 8 accurate closed-form solutions is only 0.014ms, and it can be applied efficiently in the practical on-line robot control. 