Purpose: The KOTRON-13 cyclotron was developed in South Korea and was introduced to regional cyclotron centers to produce short-lifetime medical radioisotopes. However, this cyclotron has limited capacity to produce carbon-11 isotope so far. We herein study how to develop and optimize an effective carbon-11 target system in the KOTRON-13 cyclotron by changing cooling system, combing with fluorine-18 target and evaluating beam currents. Materials and Method: To develop the optimal carbon-11 target and an effective cooling system, we designed the carbon-11 target system by Stopping and Range of Ions in Matter (SRIM) simulation program and considered the cavity pressure during irradiation at target grid. In this investigation, we evaluated the yield of carbon-11 production at different beam currents and the stability of the operation of the KOTRON-13 cyclotron. Results: The production of carbon-11 was enhanced from about 1.700 mCi ($50{mu}A$) to 2,000 mCi ($60{mu}A$) on the carbon-11 target which developed by seoul national university bundang hospital (SNUBH) and Samyoung Unitech. Additionally, the cooling condition was showed stable to produce carbon-11 under high beam current. Conclude: The carbon-11 target system of the KOTRON-13 cyclotron was successfully developed and improved carbon-11 production. Consequently, the operation of carbon-11 target system was highly effective and stable compare with other commercial cyclotrons. Our results are believed that this optimal carbon-11 target system will be helpful for the routine carbon-11 production in the KOTRON-13 cyclotron.