<p>In this article, we study a behavioral robust mean-variance portfolio selection model involving an intractable claim, which may not be directly associated with the underlying financial market but can significantly impact the terminal payoff. Also, an investor often overestimates small probabilities and underestimates large ones due to different attitudes toward gains and losses. This behavioral phenomenon of the investor is captured through a probability distortion function. We simultaneously consider a random variable representing the payoff of the behavioral investor and an intractable claim together in the terminal payoff. The distribution function of the behavioral payoff is a distorted distribution of investment payoff based on the financial market, accounting for the impact of probability distortion. We formulate a robust optimization problem by considering the worst-case scenario among all possible identically distributed random variables representing the intractable claim. By integrating the martingale method and quantile function, we analytically obtain a closed-form optimal solution of the behavioral robust mean-variance model with an intractable claim. Furthermore, we develop a numerical algorithm to compute the efficient frontiers of our models and compare their performances with an existing model that does not incorporate probability distortion.</p>