The conventional phase component method is improved by matrix similarity transformation in the paper. The equations of the faulted port network is deduced with port network theory and improved phase component model， and the relation between the elements of the faulted port impedance matrix and the port impedance is deduced from the physical meaning of the port impedance. Considering the general form of any fault， the unified fault boundary conditional equations for short-circuit and phase break up faults of double-circuit transmission lines on same tower are given. Based on the above equations， a novel algorithm is proposed to solve these equations， which is suitable for calculating any kind of simple faults on the double-circuit transmission lines on same tower. The merits of this algorithm are as following:（1） the single-line fault， interline short-circuit fault， phase break up fault and phase-to-phase fault on double-circuit transmission lines can be calculated with same model，and it is also suitable for any fault on the double-circuit transmission lines with unsymmetrical fault impedance;（2） the symmetry of the power system parameters is not required;（3） whether the common buses at both ends of the double-circuit transmission lines exist or not has no special requirement;（4） the calculation burden is decreased dramatically in contrast to the traditional phase domain method， and it is simple and practical， as well as easy to be realized by programming on computer. The results comparison between the calculation with this algorithm and EMTPE simulation shows the correctness and effectiveness of the proposed algorithm.