The Thesis aims to develop a Model Predictive Contouring Control (MPCC) algorithm for autonomous car racing. The work is conducted within the TUM Autonomous Motorsport Team, a research group from the Technical University of Munich involved in software stack development for autonomous car racing series. The MPCC is an optimal control formulation that balances tracking accuracy with a time-optimality objective for faster driving. For the developed framework, considerable attention is paid to the formulation of the optimal problem cost function, together with a novel state definition. Due to the nature of MPCC, a time-optimality constraint has to be introduced in the cost function definition, with respect to a more classic trajectory-tracking NMPC scheme.