Peak statistics from weak gravitational lensing have been shown to be a promising tool for cosmology. Here we propose a new approach to predict weak lensing peak counts. For an arbitrary cosmology, we draw dark matter halos from the halo mass function, and calculate the number of peaks from the projected halo mass distribution. This procedure is much faster than time-consuming N-body simulations. By comparing these “fast simulations” to N-body runs, we find that the peak abundance is in very good agreement. Furthermore, our model is able to discriminate cosmologies with different sets of parameters, using high signal-to-noise peaks (≳ 4). This encourages us to examine the optimal combinations of parameters to this approach in the future.