Improving the estimation accuracy for the energy consumption of electric vehicles (EVs) would greatly contribute to alleviating the range anxiety of drivers and serve as a critical basis for the planning, operation, and management of charging infrastructures. To address the challenges in energy consumption estimation encountered due to sparse Global Positioning System (GPS) observations, an estimation model is proposed that considers both the kinetic characteristics from sparse GPS observations and the unique attributes of EVs: (1) work opposing the rolling resistance; (2) aerodynamic friction losses; (3) energy consumption/generation depending on the grade of the route; (4) auxiliary load consumption; and (5) additional energy losses arising from the unstable power output of the electric motor. Two quantities, the average energy consumption per kilometer and the energy consumption for an entire trip, were focused on and compared for model fitness, parameter, and effectiveness, and the latter showed a higher fitness. Based on sparse GPS observations of 68 EVs in Aichi Prefecture, Japan, the traditional linear regression approach and a multilevel mixed-effects linear regression approach were used for model calibration. The proposed model showed a high accuracy and demonstrated a great potential for application in using sparse GPS observations to predict the energy consumption of EVs.