This paper proposes a route planning problem for sightseeing with fuzzy random variables based on constraints of required traveling times and satisfactions of the total sightseeing activity. In general, traveling times among sightseeing places and the satisfactions of activities depend on weather and climate conditions. Tourists will like to do their favorable route planning without drastically changing the tour route of usual condition such as fine even if the weather condition changes for the worse. Therefore, the fuzzy random variables for traveling times and satisfactions of activities derived from uncertainty conditions are introduced, and a new route planning problem is proposed to obtain the favorable route similar to the optimal route under the usual condition. As a basic case of fuzzy numbers, interval values and the order relation are introduced. From the order relation, the proposed model is transformed into an extended model of network optimization problems. A numerical example is provided to compare the proposed model with standard route planning problems for sightseeing.