In the article here is up-to-dated the problem of creation and implementation of the complex system on measurement and assessment of the teachers' competences. Here are presented approaches and approbations of the computer test as a means to assess formation of the teacher's metasubject competences on the example of researching of the group of teachers working with gifted children and youth. Here is revealed the theoretical basis of the competence-based approach, its basic concepts--competence and competency, metasubject competence. The level of methodological bases readiness of the competence-based approach in the aspect of organization of the pedagogical measurement process of the teacher's professional competences is provided. The review of a number of methods and means to assess the teacher's competences is presented, features of the computer competence-based oriented test as a special complex evaluation means are presented, which will provide detection of deficits of the teacher's professional competences and will allow creating conditions for development its realization in the teacher's professional activity of its cognitive, behavioural and valuable components. The description of the computer test is provided: approaches to develop the system of test tasks, determination of their contents, forms and options of representation, results of testing, working conditions with a set of tasks. Screenshots of some pages of the computer test are shown, the operation algorithm, approaches to formation and interpretation of the basis of statistics, the form of presenting recommendations on work with testing results are described. Results of the test approbation on the group of 96 teachers working with gifted children and youth are provided. The subject of testing is a cluster of the teacher's metasubject competences including communicative, research, motivating, organizing, information, creative, tutorial, methodical competences and the self-improvement competence. Analysis results of tests are provided in the aspect of mean scores, generalized characteristics of formation of teachers' competences and also generalized characteristics of professional deficits, which respondents have. In outputs of the article the conclusion is made that the offered computer test allowed not only evaluating the level of formation of competences, but also to define teachers' professional deficits and to reveal measures to eliminate these deficits.