A new algorithm for obtaining the critical tube diameter and intercept factor of parabolic trough solar collectors (PTCs) under the condition of tube alignment error has been developed theoretically, which, compared with the Monte Carlo Ray Tracing (MCRT) method, reduces the computing time remarkably. The results produced by the proposed method comply very well with the results obtained by MCRT. The critical tube diameters for different alignment errors can be precisely calculated using the algorithm, which can also be used to explain well the variation of optical efficiency. Effects of structural parameters on the optical performance are also discussed comprehensively. It is revealed that the offset direction that is perpendicular to the focus-edge connection line is most likely to cause rays-escaping. There exists an aperture width range (and also focal length range) in which the optical efficiency decreases with increasing offset angle, which is contrary to the conclusion presented in previous literature that the effects of X-direction offset (a = 0 degrees) is greater than that in Y-direction (a = 90 degrees). The proposed algorithm establishes the foundation for further geometric study on the coupling effects of multi-errors on PTCs' performance, and can also be used for quick calculation and analysis in practice. (C) 2017 Published by Elsevier Ltd.