In (Bor in Int. J. Math. Math. Sci. 17:479-482, 1994), Bor has proved the main theorem dealing with vertical bar(N) over bar ,p(n)vertical bar(k) summability factors of an infinite series. In the present paper, we have generalized this theorem on the phi - vertical bar A,p(n)vertical bar(k) summability factors under weaker conditions by using an almost increasing sequence instead of a positive non-decreasing sequence.