Based on the good chaotic properties of tangentdelay ellipse reflecting cavitymapping system (TDERCS), a kind of novel substitution boxes were constructed. The cryptographic properties, such as bijection, nonlinearity, strict avalanche, independence of output bits, the differential approximation probability and the nonlinear approximation probability of the Sbox are analyzed. The investigation method for the strength of the Sbox with the discrete chaotic system proposed by Kocarev is discussed. Theoretical analysis and backtesting results show that the method is efficient and easy to put into practice, while the constructed Sboxes show better cryptographic properties than the Sboxes based on other chaotic system, which can be used to improve the existing encryption scheme.