In this paper, we take up Taylor means to study the degree of approximation of $f\in H(\alpha,p)$ space in the generalized Hölder metric and obtain a general theorem which is used to obtain a few more results that improve upon some earlier results obtained by Mohapatra, Holland and Sahney [J. Approx. Theory 45 (1985), 363-374] in $L_p$-norm, Mohapatra and Chandra [Math. Chronicle 11 (1982), 89-96] in Hölder metric and Chui and Holland [J. Approx. Theory 39 (1983), 24-38] in sup-norm.