Self-consistent field theory (SCFT) is presented to study the adsorption of flexible polyelectrolytes (PE) onto uniformly oppositely charged cylinders. We focus on the curvature effect of adsorbing surface on the adsorption-depletion phase-transition-like behavior. Numerical solutions for SCFT functions are derived. In terms of the scaling expression (C-salt* similar to p(alpha)sigma(beta)) of the critical quantities, i.e., the salt concentration C-salt*, the charge fraction p of PE chain and the area density of surface charge a, at the adsorption-depletion transition point, we divide the whole curvature dimension into two regimes, i.e., the planar regime and the cylindrical regime. In particular, we have numerically determined the crossover point of the two regimes at which the cylinder radius r(0) approximately equates to 2 times the gyration radius R-g of PE chain, or, r(0) similar to 2R(g). In the planar regime (r(0) > 2Rg), the scaling expression is invariable with surface curvature and is reduced to the planar case, or C-salt* similar to (p sigma)(2/3). In the cylindrical regime (r(0) < 2R(g)), the exponents in the scaling expression increase as r(0) decreases and - C-salt* similar to p(0.78)sigma(0.86) for a large surface curvature r(0) = 0.1R(g). Moreover, we find a critical line for the dependence of the critical radius of cylinder on the salt concentration, which separates the adsorption and depletion states. The theoretical results are in good agreement with the Monte Carlo simulations and the experimental results.