Approximate Bayesian computation (ABC) is a family of computational techniques in Bayesian statistics. These techniques allow to fit a model to data without relying on the computation of the model likelihood. They instead require to simulate a large number of times the model to be fitted. A number of refinements to the original rejection-based ABC scheme have been proposed, including the sequential improvement of posterior distributions. This technique allows to decrease the number of model simulations required, but it still presents several shortcomings which are particularly problematic for costly to simulate complex models. We here provide a new algorithm to perform adaptive approximate Bayesian computation. We present a modification of the PMC-ABC algorithm proposed by Beaumont et al. (2009). We compare this new algorithm with the population Monte Carlo ABC algorithm of Beaumont et al. (2009), the replenishment SMC ABC algorithm of Drovandi and Pettitt (2011) and the adaptive SMC ABC algorithm of DelMoral et al. (2011) on a toy example. Finally, we apply our new algorithm to a complex individual-based social model, the PRIMA model. We show that our algorithm outperforms the three other algorithms in the two applications by requiring less simulations to reach the same posterior density quality.