Observations to precise levelling nets contain different types of error because it has been caried out with various instruments and techniques, and also completed through long period. In order to establish a precise levelling nets, therefore, the weight function has to be selected adequately in the adjustment of nets. The purpose of the study is to determine a suitable weight function for the first order geodetic levelling nets in Korea and, therefore, the various numerical tests are performed with different statistical error models. The result of the study shows that the weight function, W＝1/$L^2$ is more efficient than W＝1/L in the first order levelling nets in the Korea.