Compared with the integer order differential operator，fractional order operator can describe some charac-teristics of the system more accurately，such as hereditary and memory properties． In order to find a more accurate and efficient way to solve the fractional order system，a new computational scheme designed to get the system re-sponse was put forward based on Adams-type scheme and the Newmark-β method． The inverse problem of parame-ter identification was considered as a nonlinear optimization problem． And the enhanced response sensitivity method was used to solve the identification equation． Numerical examples show that the calculation format of the direct problem proposed in the paper can quickly and accurately get response from the system，so the enhanced response sensitivity method can accurately identify the parameters of the fractional system and be insensitive to the measure-ment noise．