This paper introduces a dynamic network model together with a phasor measurement unit (PMU) measurement model suitable for power system state estimation under spoofing attacks on the global positioning system (GPS) receivers of PMUs. The spoofing attacks may introduce time-varying phase offsets in the affected PMU measurements. An algorithm is developed to jointly estimate the state of the network, which amounts to the nodal voltages in rectangular coordinates, as well as the time-varying attacks. The algorithm features closed-form updates. The effectiveness of the algorithm is verified on the standard IEEE transmission networks. It is numerically shown that the estimation performance is improved when the dynamic network model is accounted for compared with a previously reported static approach.