Voltage-sensorless control has been investigated for Voltage Source Inverters (VSIs) for many years due to the reduced system cost and potentially improved system reliability. The VSI based Resistive Active Power Filters (R-APFs) are now widely used to prevent the harmonic resonance in power distribution network, for which the voltage sensors are needed in order to obtain the current reference. In this paper a grid-voltage-sensorless control strategy is proposed for the R-APF with series LC-filter. Unlike the traditional resistance emulation method, this proposed control method re-shapes the output impedance of the R-APF at the harmonic frequencies, which is independent of the current reference. A fundamental grid voltage estimation method is also proposed to control the DC-link voltage. The performance of the proposed control method is verified in both simulations and experiments. The results show good accuracy of the emulated resistance and functionality of the DC-link voltage control. With the proposed method, the cost of the R-APF can also be reduced with potentially improved system reliability.