Negative sequence pilot protection（NSPP） is one of the most frequently adopted protective principles in HV/EHV transmission lines for its capability of protecting the whole fault process， being immune from the distributed capacitance and system disturbance. But its extensive application is affected by its incapability of the open-phase operation mode. To remedy such a situation， a novel algorithm for NSPP in open-phase transmission lines is proposed which works by adopting the phase voltage and current vectors in three stages of operation in the transmission line-load operation， open phase operation and fault occurrence in open phase， to calculate the imaginary negative sequence voltage on the bus side， and the negative sequence current with compensation to the negative sequence component existing in open-operation lines. Then the NSPP can accurately judge the fault direction while providing full-time protection to the transmission line， simplifying the microprocessor based NSPP relay and improving its reliability.