In this study, the peridynamic Drucker-Prager plastic model with fractional order derivative is proposed to investigate the plastic behavior of surrounding rocks around tunnels, in which the Caputo fractional derivative is employed due to its mathematical simplicity. Instead of utilizing just one parameter for the typical nonassociated flow rule, such as dilation angle, multiple parameters, such as fractional order and interval of fractional derivative, are used to specify the direction of plastic deformation, and the fractional derivative based-typical flow rule is proposed. As a result, compared with the traditional peridynamic Drucker-Prager plastic model, the proposed method is a more generalized model including the typical nonassociated flow rule. Besides, based on the PD force density, the strategy of exertion of initial stress is proposed to simulate in-situ stress in rocks. Taking a block subjected to compression as an example, the impacts of various factors, such as fractional order and interval of fractional derivative, are investigated. A numerical simulation of tunnel excavation in rocks is carried out and the numerical results obtained by the proposed method are verified by comparing with FEM results.