We present results on cavity-photon-assisted electron transport through two lateral quantum dots embedded in a finite quantum wire. The double quantum dot system is weakly connected to two leads and strongly coupled to a single quantized photon cavity mode with initially two linearly polarized photons in the cavity. Including the full electron-photon interaction, the transient current controlled by a plunger-gate in the central system is studied by using quantum master equation. Without a photon cavity, two resonant current peaks are observed in the range selected for the plunger gate voltage: The ground state peak, and the peak corresponding to the first-excited state. The current in the ground state is higher than in the first-excited state due to their different symmetry. In a photon cavity with the photon field polarized along or perpendicular to the transport direction, two extra side peaks are found, namely, photon-replica of the ground state and photon-replica of the first-excited state. The side-peaks are caused by photon-assisted electron transport, with multiphoton absorption processes for up to three photons during an electron tunneling process. The inter-dot tunneling in the ground state can be controlled by the photon cavity in the case of the photon field polarized along the transport direction. The electron charge is delocalized from the dots by the photon cavity. Furthermore, the current in the photon-induced side-peaks can be strongly enhanced by increasing the electron-photon coupling strength for the case of photons polarized along the transport direction.