Road network is usually stochastic and time-dependent and reliable shortest path finding problem is a sub-problem dynamic traffic assignment model, which is a valuable tool in intelligent transport systems. Different travelers have different route choice preferences, such as time budget and travel cost, which may involve multiple conflicting objectives. A new reliable shortest path finding model is proposed in this paper to find reliable shortest paths in stochastic and time-dependent road networks considering time budget and travel cost. A modified non-dominated sorting genetic algorithm is used to solve this model and its parameters are set by the Taguchi method. A case study of road network consisted of main streets in Beijing is demonstrated to examine that the proposed algorithm perfectly provides a set of reliable shortest paths to facilitate travelers’ decisions based on their attitudes toward time budget and travel cost.