In this article, we present a novel tension distribution algorithm for cable-driven parallel robots (CDPRs) with two degrees of actuation redundancy. The algorithm consists of calculating the tension feasible region (TFR) and optimizing the tension distribution. The TFR has been innovatively calculated without relying on the convex hull method. The topological relationship of the vertices is maintained, so the calculation steps are greatly reduced. For optimizing TFR, various functions are proposed, especially the tension robustness index is defined. We prove the complexity and continuity of the algorithm and we study several examples. The results are compared with those obtained with the existing state-of-the-art method, and the proposed technique is shown to be more computationally efficient. The robustness of the optimal solution is also calculated. The proposed algorithm can be applied in some real-time systems with unmeasurable interference, such as interactive devices.