In single-phase grid-connected inverters, precise and fast detection of the phase angle is essential to guarantee the correct generation of the reference signals. In order to detect the phase angle, SRF-PLL system has been widely used in the grid-connected inverter. However, in contrast with three-phase grid-connected inverter system, single-phase grid-connected inverters are difficult to acquire the information of phase angle and frequency. Hence, using an all-pass filter can make a virtual grid voltage, which is shifted 90-degree from the grid voltage. However, the phase error can be generated due to the characteristics of all-pass filter when the grid frequency is varying. In this paper, the effects of output current and synchronous dq-axis voltages due to the phase error caused by non-ideal all-pass filter are analyzed in detail. The effectiveness of the proposed algorithm is verified through simulation and experiment results.