In this paper, we establish two new results related to the stability and uniform boundedness of the following non-autonomous Liénard type equation with a variable deviating argument $r(t)$: \begin{eqnarray*} &&x^{\prime\prime}(t) + f(t, x(t), x(t − r(t)), x^\prime (t), x^\prime (t − r(t)))x^\prime (t) + g_1(x(t)) \\&&+g_2(x(t − r(t))) = p(t, x(t), x(t − r(t)), x^\prime (t), x^\prime (t − r(t))),\end{eqnarray*} when $p(.) \equiv 0$, and $p(.) \not = 0$, respectively. By the Lyapunov functional approach, we prove our results and give an example to illustrate the theoretical analysis in this work. By this work, we extend and improve an important result in the literature.