Summary: This paper considers the existence of a global smooth solution to the initial boundary value problem to a quasilinear hyperbolic equation \[ u_t+\left(\frac 12 u^2\right)_x= -\frac{u^2}{x}\tag{1} \] with singularity at \(x=0\). Applying a function transformation, it transforms (1) into a regular hyperbolic equation. Then, by using the maximum principle of the first-order quasilinear hyperbolic system established by C. Zhu [Proc. R. Soc. Edinb., Sect. A 125, No. 6, 1277–1285 (1995; Zbl 0843.73033)], it obtains \(C^1\)-norm estimates to the corresponding problem and proves the existence of global smooth solution to the initial boundary value problem.