In this paper, we study the existence of periodic solutions to the following prescribed mean curvature Li\'{e}nard equation with a singularity and a deviating argument $$(\frac{u'(t)}{\sqrt{1+(u'(t))^2}})'+f(u(t))u'(t)+g( u(t-\gamma))=e(t)$$ And by applying Mawhin's continuation theorem, a new result on the existence of positive $T-$periodic solution for this equation is obtained. An example is given to illustrate the effectiveness of our results. Our research enriches the contents of prescribed mean curvature equations.
