Approximate Bayesian Computation is widely used to infer the parameters of discrete-state continuous-time Markov networks. In this work, we focus on models that are governed by the Chemical Master Equation (the CME). Whilst originally designed to model biochemical reactions, CME-based models are now frequently used to describe a wide range of biological phenomena mathematically. We describe and implement an efficient multi-level ABC method for investigating model parameters. In short, we generate sample paths of CME-based models with varying time resolutions. We start by generating low-resolution sample paths, which require only limited computational resources to construct. Those sample paths that compare well with experimental data are selected, and the temporal resolutions of the chosen sample paths are recursively increased. Those sample paths unlikely to aid in parameter inference are discarded at an early stage, leading to an optimal use of computational resources. The efficacy of the multi-level ABC is demonstrated through two case studies.