Abstract: A new high-order associative memory system via Tchebycheff interpolation is proposed. It offers the error-free approximation to multi-variable polynomial functions with arbitrarily given order. Tchebycheff interpolation nears to the best uniform approximation, this ensures theoretically the approximation precision as a whole to multi-variable continuous functions with arbitrarily given order. Particularly, comparing with other AMS, it also has distinctive advantage in approximation to some discontinuous functions such as rectangular pulse function. Theoretic analysis and numerical simulations have shown that the proposed TI-AMS has the advantages in much less computational, high-precision of learning, fast convergence rate and much less required whole memory size. It has great potential in the application areas of picture compression, pattern recognition, and controller implementation for high-precision real-time intelligent control.