Vocational and technical education professional courses have significant occupational relevance, and the teaching and evaluation design ideas of its course Civics should be drawn by the job tenure demand. In this paper, through the matching comparison between the characteristics of graduates of higher vocational colleges and the vector space of job demand characteristics, the residual optimal algorithm is used to construct the matching model of college students’ supply and demand so as to achieve the maximization of the total matching value between supply and demand. On the basis of the CIPP evaluation model and the teaching characteristics of courses in higher vocational colleges and universities, a fit analysis is carried out to construct the evaluation index system for the teaching of Civics and Politics in courses in higher vocational colleges and universities. The study shows that the weights of the four first-level indicators, namely, teaching background, teaching input, teaching process, and teaching effect, are 0.2042, 0.2592, 0.3754, and 0.1612, respectively, of which the teaching process has the most significant proportion of weight. Practical value can be gained from the teaching evaluation system.