We determine the characteristic of dissipative quantum transport in a coupled qubit network in the presence of on-site and off-diagonal external driving. The work is motivated by the dephasing-assisted quantum transport where noise is beneficial to the transport efficiency. Using Floquet-Magnus expansion extended to Markovian open systems, we analytically derive transport efficiency and compare it to exact numerical results. We find that driving may increase the efficiency at frequencies near the coupling rate. On the contrary, at some other frequencies the transport may be suppressed. We then propose the enhancement mechanism as the ramification of interplay between driving frequency, dissipative, and trapping rates.