The article presents a method of increasing the shape and dimensional accuracy of low-stiffness shafts manufactured in a single pass of a grinding wheel in traverse grinding. One-pass manufacturing is one of the ways for reducing machining time and increasing efficiency, thus lowering production costs. However, maintaining the necessary accuracy proves to be a challenge because the whole machining allowance has to be removed at once, leaving no room for errors that could be fixed in additional passes of the tool. It is especially true in finishing operations, such as traverse grinding. In addition, grinding the workpiece in a single pass of a grinding wheel leads to high forces, which cause elastic deformation of the part. The lower the stiffness of the part, the more difficult it is to achieve the required accuracy. As a result, there are many methods of improving the accuracy of grinding such parts, but they tend to be either expensive or reduce the machining efficiency. Thus, it is important to seek new methods that would allow improving the accuracy of the machining without reducing its efficiency. The proposed method does not require using steady rests and is based on the measurement of the normal grinding force component. Knowing the value of the grinding force when grinding with a set grinding depth, the elastic deformation of the machine tool–tool–workpiece system is calculated in each position of the grinding wheel. Based on the calculated deformation, the additional infeed of the grinding wheel is implemented in order to stabilise real grinding depth and to increase the accuracy of the produced part. The experimental tests were conducted to prove the effectiveness of the proposed method.