We studied the dynamics of electrons generated by two-step photoexcitation in an intermediate-band solar cell (IBSC) comprising InAs/GaAs/AlGaAs dot-in-well (DWELL) structure using time-resolved photocurrent (TRPC) measurement. The examined IBSC exhibited considerably slower photocurrent decay than a conventional InAs/GaAs quantum dot IBSC, which is due to the extraordinarily long-lived electrons in the DWELL. In order to retrieve the electron lifetime from the decay profile, we developed a model reproducing the observed decay and performed parameter fitting. The fitting results indicate that the electron lifetime in the DWELL is approximately 30 μs. In the two-colour excitation TRPC measurement, we found that an additional infrared (IR) light accelerates the photocurrent decay while the photocurrent increases by approximately 3%, because the additional IR light causes two-step photoexcitation of electrons in the DWELLs towards the conduction band. Furthermore, we demonstrated that the open-circuit voltage increases with increasing of the contribution of the second IR excitation process.