To eliminate current harmonics and to obtain enhanced dynamic behaviors, the voltage feedforward scheme is normally adopted in the control process of transformerless grid-tied converters. However, voltage measurement errors caused by parameter variation of sampling resistance and zero-voltage drift in analog devices will result in DC current injection and distorted grid currents in grid-tied systems. Conventional compensation strategies based on plug-in repetitive controllers and multiple resonant controllers are considered to be effective solutions to solve this problem. Even though undesired components in grid currents can be partially mitigated with these conventional compensation schemes adopted, degraded reference-tracking process with oscillations and slow dynamics are inevitably caused by the controller coupling. To obtain decoupling between reference tracking and disturbance rejection, this paper proposes a dual-loop controller to achieve current regulation and to suppress the disturbances caused by voltage measurement errors. With the proposed dual-loop controller adopted, DC current injection and distortion of grid currents can be effectively attenuated while excellent transient performance with negligible overshoot and fast step response can be simultaneously guaranteed. Frequency-domain analysis and experimental validations are both conducted to verify the effectiveness of the proposed strategy.