The effect of current screen layer on the bias voltage dependence of a magnetoresistive (MR) ratio was studied for a Heusler alloy-based current perpendicular-to-plane giant-magnetoresistive (CPP-GMR) sensor. The MR ratio was improved by using the current screen layer for the Heusler alloy based CPP-GMR sensor. In addition, the bias voltage dependence of the MR ratio was also improved. This improvement in bias voltage dependence appears to be due to the suppression of the magnetic moments fluctuation near a pinhole which reduces the spin-torque effect.