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In the paper, we give an existence theorem of periodic solution for Liénard equation $\dot{x}=y-F\left(x\right)$, $\dot{y}=-g\left(x\right)$. As a result, we estimate the amplitude $\rho \left(\mu \right)$ (maximal $x$-value) of the limit cycle of the van der Pol equation $\dot{x}=y-\mu (x^3/3-x)$, $\dot{y}=-x$ from above by $\rho \left(\mu \right)<2.3439$ for every $\mu \ne 0$. The result is an improvement of the author’s previous estimation $\rho \left(\mu \right)<2.5425$.