This paper addresses a time-dependent green vehicle routing problem (TDGVRP) with the consideration of traffic congestion. In this work, the objective is to optimize the vehicle routing plan, with the goal of reducing carbon emissions, which has linear relationship with fuel consumption of vehicles. To deal with traffic congestion, travel time are considered to be time-dependent. We propose a branch-and-price (BAP) algorithm to precisely solve this problem. A tailored labeling algorithm is designed for solving the pricing sub-problem. Computational experiments demonstrate the effectiveness of the proposed BAP algorithm.