The article notes the relevance of the quality management systems implementation of engineering sphere enterprises in the context of the international standard ISO 9001:2015 requirements and it was substantiated that an internal audit is means of improving them. The main problems of internal audits of enterprises quality management systems, which are related with a formal approach to their conduct are identified and the negative consequences for companies regarding doing business are defined. The existing interpretations of «internal audit» concept are considered and the expediency of modern approach applying to its compliance with the requirements of ISO 9001:2015 is substantiated. The author focuses on the new version of international standard ISO 19011:2018 «Guidelines for auditing management systems» requirements and provides the principles for internal audits conducting, compliance with which is directed on their effective implementation. A flowchart of quality management system audits conducting is given and significant aspects of influence on ensuring of their improvement are considered. The systemic inconsistencies of the quality management system of an engineering enterprise, based on the internal audits results of 2012–2017, are formed, and focuses on activities for their elimination. Emphasis is placed on the expediency of applying the algorithm created by the author for internal audits conducting of the quality management system of an engineering enterprise as a tool to ensure of his effectiveness and objectivity. The cause-and-effect Ishikawa diagram using in combination with the Pareto analysis with the aim of a competent approach to eliminating the inconsistencies of the quality management system of an engineering enterprise, which were identified in the process of internal audits conducting has been proposed.