The multi-sampling technique is an effective solution to reduce the delay in digital-controlled power converters. However, this solution may deteriorate the dynamic performance of converters due to vertical crossing (VC) between the modulation signal and the carrier signal, which changes the small-signal PWM gain. This paper proposes a model of the VC for the multi-sampled single-phase grid-connected converter, which specifies the piecewise linear relationship between the small-signal PWM gain and the duty ratio. Then a control scheme is proposed to eliminate the VC by adaptively adjusting the phase of the carrier signal. The proposed scheme features better dynamic performance than existing methods. Finally, the theoretical analysis is validated by the simulation and experimental results.