In this paper, a set of distributed secondary controllers is introduced that provide active regulation for both steady-state and transient-state performances of an islanded DC microgrid (MG). The secondary control for distributed converter interfaced generation (DCIG) not only guarantees that the system converges to the desired operating states in the steady state but also regulates the state variations to a prescribed transient-state performance. Compared with state-of-the-art techniques of distributed secondary control, this paper achieves accurate steady-state secondary regulations with prescribed transient-state performance in an islanded DC MG. Moreover, the applicability of the proposed control does not rely on any explicit knowledge of the system topology or physical parameters. Detailed controller designs are provided, and the system under control is proved to be Lyapunov stable using large-signal stability analysis. The steady-state and transient-state performances of the system are analyzed. The paper proves that as the perturbed system converges, the proposed control achieves accurate proportional power sharing and average voltage regulation among the DCIGs, and the transient variations of the operating voltages and power outputs at each DCIG are regulated to the prescribed transient-state performance. The effectiveness of the proposed control is validated via a four-DCIG MG system.