A constructal thermodynamic optimization model for ocean thermal energy conversion system (OTECS) with a dual-pressure organic Rankine cycle (DPORC) to make better use of the ocean thermal energy is established in this paper. It is performed by combing constructal theory with finite time thermodynamics. Optimal design of the OTECS is conducted under the conditions of the fixed total heat transfer area of the heat exchangers and the total volume of the dual-pressure turbines. The net power output of the OTECS is chosen as the optimization objective, and six parameters, that is, the heat transfer plate effective lengths of the high-temperature evaporator, low-temperature evaporator, and condenser, volume fraction of the high-pressure turbine as well as heat transfer area fractions of the condenser and high-temperature evaporator, are employed as the optimization variables. The optimal performance and optimal construct of the OTECS are obtained. The influences of total mass flow rate and mass flow rate ratio of the working fluid, inlet temperatures of the warm and cold seawaters, and wheel diameter ratio of the turbine on the optimization results are analyzed. Moreover, the optimal performances of the OTECS with the DPORC and single-pressure organic Rankine cycle (SPORC) are compared. The results show that the net power outputs after the primary, twice, triple, and sextuple constructal thermodynamic optimizations are improved by 2.80%, 4.66%, 9.95%, and 14.95%, respectively, compared with the initial net power output. The net power output can be further improved by increasing the total mass flow rate of the working fluid, warm-seawater inlet temperature, and wheel diameter ratio of the turbine in reasonable ranges. Compared with the SPORC, the DPORC has advantages in both the net power output and net thermal efficiency. The obtained results can provide theoretical guidelines for the optimal designs of the OTECS.