This paper introduces a new variant of the electric vehicle routing problem, named PEVRP for Periodic Electric Vehicles Routing Problem, in which the routing and charging are planned over a multi-period horizon, subject to frequency constraints, limited fleet of electric vehicles available at the depot, intermediate facilities for charging during the trips, and partial charging. The objective of the PEVRP is to minimize the total cost of routing and charging over the time horizon, such that each vehicle could be charged nightly at the deport, and during the day at charging stations if refuelling is necessary. We propose two constructive heuristics. The first one is based on clustering technique that aims at allocating customers per vehicle and per period, and then constructs tour for each vehicle visiting customers and charging stations for refuelling. The second one is based on best insertion strategy, in which each customer is allocated to its best position that minimizes charging a nd routing cost. Using several parameters setting, we compared and analysed the results of the two proposed approaches on 50 new instances derived from EVRP instances of the literature.