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In this paper we study the semileptonic decays of $B_c^- \to(\eta_c,J/\psi)l^-\bar\nu_l$. We firstly evaluate the $B_c \to (\eta_c,J/\Psi)$transition form factors $F_0(q^2)$, $F_+(q^2)$, $V(q^2)$ and $A_{0,1,2}(q^2)$by employing the pQCD factorization approach, and then we calculate thebranching ratios for all considered semileptonic decays. Based on the numericalresults and the phenomenological analysis, we find that: (a) the pQCDpredictions for the values of the $B_c \to \eta_c$ and $B_c \to J/\Psi$transition form factors agree well with those obtained by using other methods;(b) the pQCD predictions for the branching ratios of the considered decays are$Br\left(B_c^- \to\eta_c e^-\bar\nu_e(\mu^-\bar\nu_\mu)\right)=(4.41^{+1.22}_{-1.09})\times10^{-3}$, $Br\left(B_c^-\to\eta_c\tau^-\bar\nu_\tau\right) =(1.37^{+0.37}_{-0.34})\times10^{-3}$,$Br(B_c^- \to J/\Psi e^-\bar\nu_e(\mu^-\bar\nu_\mu))=(10.03^{+1.33}_{-1.18})\times10^{-3}$, and $Br\left(B_c^- \toJ/\Psi\tau^-\bar\nu_\tau\right) =(2.92^{+0.40}_{-0.34})\times10^{-3}$; and (c)we also define and calculate two ratios of the branching ratios $R_{\eta_c}$and $R_{J/\Psi}$, which will be tested by LHCb and the forthcoming Super-Bexperiments.

Semileptonic decays $B_c\to(\eta_c,J/\Psi)l\nu$ in the perturbative QCD approach