The classical Shewhart NP control chart is used widely in industrial and service practice for the relative simplicity of handling attribute quality characteristics. However, the static strategies become less and less adequate for today's highly competitive industrial society because of their low efficiency to detect slight process changes promptly. To improve the capability of control charts, some adaptive schemes, such as variable sample size (VSS), variable sample interval (VSI), and variable control limits (VCL), have been extensively studied in the recent decade. In this paper, we propose a new VSS NP control chart with adjusting sampling inspection (called ASI-NP chart) and give the performance analysis using Markov chain. As the optimal model is related to an integer nonlinear program, genetic algorithms (GAs) are involved and Taguchi experiments are applied to configure the parameter of the GAs in numerical examples. The comparison study between classical NP chart and ASI-NP chart is conducted, and the result shows that ASI-NP chart's performance characteristics are significantly better than those of classical NP charts in all situations, especially, in processes with slight shift and high quality.