The moment when Electrical Vehicle (EV) starts charging or discharging is one of the most important parameters in estimating the impact of EV load on the grid. In this paper, a decision-making problem of determining the start time of charging and discharging during allowed period is proposed and studied under the uncertainty of real-time price. Prospect theory is utilized in the decision-making problem of this paper for it describes a kind of decision making behaviors under uncertainty. The case study uses the parameters of Springo SGM7001EV and adopts the historical realtime locational marginal pricing (LMP) data of PJM market for scenario reduction. Prospect values are calculated for every possible start time in the allowed charging or discharging period. By comparing the calculated prospect values, the optimal decisions are obtained accordingly and the results are compared with those based on Expected Utility Theory. Results show that with different initial State-of-Charge ($SoC_0$) and different reference points, the optimal start time of charging can be the one between 12 a.m. to 3 a.m. and optimal discharging starts at 2 p.m. or 3p.m. Moreover, the decision results of Prospect Theory may differ from that of the Expected Utility Theory with the reference points changing.