We consider the vector perturbation (VP) precoder design for multiuser multiple-input single output (MU-MISO) broadcast channel systems which is robust to power scaling factor errors. VP precoding has so far been developed and analyzed under the assumption that receivers could have known the power scaling factor in advance of tranmission perfectly, which is hard to obtain due to the large dynamic range and limited feedforward. However, as demonstrated in our results the performance of VP precoding is quite sensitive to the accuracy of power scaling factor and always encounter an error floor at mid to high signal-to-noise ratio (SNR) regimes. Motivated by such observations, we propose a robust VP precoder based on the minimum mean square error (MMSE) criterion. Simulation results show that, the robust VP precoder outperforms conventional VP precoding designs, as less sensitive to power scaling factor errors.