The magnetoresistance (MR) of Co film and Co/Pt bilayers was studied systematically as a function of Co and Pt thickness at room temperature. In the samples with the wedge shape, we found the unidirectional MR which has the characteristics of RMz≠R(−Mz) with the magnetization normal to the film. The measured unidirectional MR is attributed to the differential anomalous Hall resistance due to the thickness difference at the electrodes for the longitudinal resistance measurements. The unidirectional MR effect in the Co/Pt bilayers can be greatly suppressed by a non-magnetic Cu inserting layer.