Fuzzy set theory has been applied to build various portfolio selection models in the past decades. Based on the knowledge of previous studies, this paper proposes a new portfolio selection model with technical pattern-based fuzzy birandom variables. There are two innovations in the work: The concept of technical pattern is combined with fuzzy set theory to use the fuzzy birandom variables as security returns; The fuzzy birandom Value-at-Risk (VaR) is introduced to build the mathematical model, named the fuzzy birandom VaR-based portfolio selection model (FBR-PSM). Then, fuzzy simulation is extended to the fuzzy birandom case to obtain a general solution to the FBR-PSM, which is called as fuzzy birandom simulation-based particle swarm optimization algorithm (FBS-PSO). To illustrate the performances of the FBR-PSM and the FBS-PSO, two numerical examples are introduced based on investors' different risk attitudes. Finally, we analyze the experimental results and provide further discussions.