Though the blind super-resolution problem is nonconvex in nature, recent advance shows the feasibility of a convex formulation which gives the unique recovery guarantee. However, the convexification procedure is coupled with a huge computational cost and is therefore of great interest to investigate fast algorithms. To do so, we adapt an operator splitting approach ADMM and combine it with a novel preconditioning scheme. Numerical results show that the convergence rate is significantly improved by around two orders of magnitudes compared to the currently most adopted solver CVX. Also, by a Lasso type of formulation, the proposed solver is able to keep its high resolvability even under 0 dB SNR setting.