In this paper, a general discretization of Boltzmann-BGK model equation along the characteristic line is obtained, where the time integration of collision term is handled as a weighted average between the implicit and explicit part. Moreover, the value of weight factor depends on the local Knudsen number, which represents the local flow regime and scale. With the aid of this weight factor, a scale adaptive discrete unified gas kinetic scheme (SADUGKS) has been developed based on the existing discrete unified gas kinetic scheme (DUGKS). The range of the value of weight factor is analyzed mathematically, and discussed physically. It is found that the value of weight factor could adjust dynamically according to the local flow regime and scale. Finally, four numerical simulations, including Taylor vortex flow, lid-driven cavity flow, backward-facing step flows and micro-Couette flow, are performed to investigate the accuracy and validity of SADUGKS in both continuum and rarefied flow regimes. It is concluded that the present SADUGKS is a reliable and practical multiscale method for all Knudsen number gas flows.