Summary: This paper concerns the study of the numerical approximation for the following initial-boundary value problem: \[ \begin{gathered} u_t = u_{xx}- u^{-p},\quad x\in (0, 1),\quad t\in (0, T_q),\\ u_x (0, t) = 0,\quad u_x (1, t) = 0,\quad t\in (0, T_q),\\ u(x, 0) = u_0 (x) > 0,\quad x\in [0, 1]. \end{gathered} \] Under some assumptions, we prove that the solution of a semidiscrete form of the above problem quenches in a finite time and estimate its numerical quenching time. We also prove the continuity of the quenching time as a function of the initial datum. Finally, we give some numerical experiments to illustrate our analysis.