The appropriate reference wave in single-exposure phase-shifting digital holography using a random-complex-amplitude encoded reference wave is experimentally investigated. Although the reference wave is generalized, the quality of reconstructed images depends on it. Furthermore, when the reference wave satisfies a certain condition, reconstructed images cannot be obtained in this method. After the certain condition is presented, the appropriate condition is studied using a speckle property. Experimental results are given to investigate the relations between the quality of reconstructed images and the sizes of speckles of the reference waves. The results prove that the appropriate reference wave exists in this method.