The true dc measurement of electrical field effect on the resistivity of orthorhombic TaS3 in the CDW state was performed for the first time with extremely short distances between the contacting leads. Very weak nonlinear effect was observed up to 1300 V/cm. A distinct resistivity-increasing effect was found, which can not be understood within the framework of any currently available theories. We propose a transverse tunneling model to account for this anomaly.