  This paper analyzes a time-stepping discontinuous Galerkin method for
modified anomalous subdiffusion problems with two time fractional derivatives
of orders $ \alpha $ and $ \beta $ ($ 0 < \alpha < \beta < 1 $). The stability
of this method is established, the temporal accuracy of $ O(\tau^{m+1-\beta/2})
$ is derived, where $m$ denotes the degree of polynomials for the temporal
discretization. It is shown that, even the solution has singularity near $ t
  = {0+} $, this temporal accuracy can still be achieved by using the graded
temporal grids. Numerical experiments are performed to verify the theoretical
results.
