In this work, a new variant of the approximate Bayesian computation (ABC) algorithms is presented based on the concept of the nested sampling (NS) algorithm proposed by Skilling [Ref.1] and an ellipsoidal sampling technique shown in Mukherjee et al. [Ref.2]. The ABC algorithms have been widely used for parameter estimation and model selection in different fields mainly when the likelihood function is intractable or cannot be approached in a closed form. However, those algorithms suffer from the high rejection rates during the sampling process. To overcome this problem, the authors propose a new variant of ABC algorithms called ABC-NS. The efficiency of the proposed algorithm will be compared with the ABC based on sequential Monte Carlo (ABC-SMC) sampler. The obtained results show how the ABC-NS outperforms the ABC-SMC in terms of computational efficiency while achieving the same or better results. Several examples have been proposed to illustrate the efficiency of the ABC-NS compared with the ABC-SMC for parameter estimation and model selection issues.