The performance of asynchronous fast frequency hopping-multiple access (AFFH-MA) systems with multiple hops per bit is investigated with a linear-combining receiver in Rayleigh fading. We present an accurate approximation method for evaluating the error probability by using the characteristic function, Taylor series, and Gauss-Chebyshev quadrature rule. We will show that the proposed method provides an accurate approximation, compared with a simple Gaussian approximation. The validity of proposed analytic works is verified through Monte Carlo simulations.