Portfolio management requires selecting the right underlying asset in the asset pool and determining the proportion of the portfolio. The timeliness of calculations of the portfolio models is extremely important. The L₁ norm sparse Min-CVaR (Minimum-CVaR, Conditional Value at Risk) model is able to simultaneously select the target assets and determine the capital allocation. Meanwhile, the L₁ norm sparse Min-CVaR is harder to handle owing to the L₁ norm regularization. In order to solve large-scale problems effectively, a Lagrangian dual model based on the structural features of constraints in the original model was constructed and solved by the state-of-the-art commercial solver GUROBI 12.8. Numerical experiments were conducted on the simulated data (50000 rows and 200 columns) and real-world data (the S&P 500: 28805 rows and 483 columns). The numerical results show that, compared to the primal model, the dual method is several times faster than the primal method, and it is even faster than the standard Min-CVaR portfolio selection model without regularization.