The invention discloses a sigmoid function fitting hardware circuit based on a Remez approximating algorithm. A sigmoid function fitting method is characterized by including the following steps that (1), the order of a fitting polynomial is determined; (2), a fitting interval of a sigmoid function is obtained; (3), a piecewise interval is obtained; (4), the fitting polynomial is obtained; (5), a coefficient storing module is designed; (6), a polynomial calculation module is designed; (7), a judgment module is designed; (8), the fitting hardware circuit is obtained; (9), a fitting execution interval where operands are located is judged; (10), a coefficient of the fitting polynomial is read; (11), fitting calculation is carried out in the polynomial calculation module. On the basis of reducing hardware resource consumption, the calculation accuracy is improved, the calculation speed is increased, and the flexibility of a calculation structure is promoted.