This paper deals with the degree of approximation by an operator based on the partial sum of the Fourier series of a function of class Lp,p≥1. We use modulus of continuity of the function satisfying weaker conditions than those used by Deǧer and Bayindir [On the degree of approximation by the Woronoi-Nörlund and Riesz type means in the GHM, Azerb. J. Math., 8 (2018), 122-141]. The results of our paper also improve those of Singh and Sonker [Degree of approximation of function in Hpw in generalized Hölder metric by matrix means, Mathematical modelling and scientific computation, 1-10, Commun. Comput. Inf. Sci., 283, Springer, Heidelberg, 2012].