Summary: Some new sufficient conditions ensuring that the generalized Liénard equation \(x+ f(x, x)x+ g(x)= 0\) has at least one non-zero periodic solution are obtained. Our results not only improve those in [Z. Zheng, J. Math. Anal. Appl. 148, No. 1, 1-10 (1990; Zbl 0706.34037)] but also correct an error appeared in that paper.