Pan and Wang presented a method for computing uniform Gr¨obner bases for certain ideals generated by polynomials with parametric exponents in 2006, and two criteria were proposed to determine if a uniform Gr¨obner basis can be obtained. This paper gives a new algorithmic approach for computing the uniform Gr¨obner basis such that Pan and Wang’s method could be concluded as a special case. The authors use the method of reduced term order under ring homomorphism to get the reduced uniform Gr¨obner basis. Also the authors point and correct a mistake in Pan and Wang’s method. The result is a generalization of approach of Pan and Wang and one could compute the uniform Gr¨obner basis more efficiently by the new approach.