The beginning of the Constitutional Court’s operation in the Republic of Kazakhstan marked the posing of a large number of problematic issues that require their solution both at the level of legal theory and practice. The presented article is focused on the analysis of the constitutional complaint’s institution and the formation of suggestions aimed at improving the relevant provisions of the Law of the Republic of Kazakhstan «On the Constitutional Court of the Republic of Kazakhstan» (hereinafter referred to as the Law). The author, first of all, studies the issue on the system of entities having the right to file a constitutional complaint. The author states that the current wording of the Art. 45 of the Law unjustifiably narrows the range of such entities. A constitutional complaint is currently not available to foreign citizens and stateless persons, as well as to legal entities, which, according to the author, is a manifestation of discrimination. Besides, the author studies the issue on the subject matter of a constitutional complaint – regulatory legal acts of the Republic of Kazakhstan. It is concluded that the definition of the category of «regulatory legal acts» is borrowed from the Law of the Republic of Kazakhstan «On Legal Acts», which, in turn, is improperly formulated. In particular, it does not absolutely cover all types of legal acts containing the norms of law, which, therefore, «takes» them out of the scope of the subject matter of a constitutional complaint. It is offered that the Law of the Republic of Kazakhstan «On Legal Acts» should provide an independent type of regulatory legal act – a legal act of social partnership within the system of legal acts. The author pays attention at the end of the article to the need to increase the level of consistency of certain provisions of the Art. 45 of the Law with each other. As a result of the conducted research, the author offers the paragraph 1 of Part 2 of the Art. 45 of the Law in the following wording: «the disputed law or another regulatory legal act applied by the court, directly affects the rights and freedoms in a specific case with the participation of a citizen, and a judicial act was issued in the case, which entered into legal force». In addition, some recommendations were made in regard to Part 4 of the Art. 45 of the Law. As a conclusion, the author indicates the need to take systematic steps aimed at clarifying the provisions of the Law, to establish appropriate procedures, wide informing campaign for citizens about the limits of the competence of the Court, as well as to ensure studying the discipline of «Constitutional Procedural Law» by the students.