The $PM_{10}$ concentration data is useful for indentifying intensity and a transport way of Asian dust. However, it is difficult to identify them properly due to the limited spatial resolution and coverage. Therefore, a methodology to estimate $PM_{10}$ concentration using visibility data obtained from synoptic observation was developed. To derive the converting function, correlation between visibility and $PM_{10}$ concentration is investigated using visibility and $PM_{10}$ concentration data observed at 20 stations in Korea from 2005 to 2009. To minimize bias due to atmospheric moisture, data with higher relative humidity over a critical value were eliminated while deriving $PM_{10}$-visibility relationship. As a result, an exponentially decreasing function of visibility is obtained under the condition that relative humidity is less than 82%. Verification of the visibility converting function to $PM_{10}$ concentration was carried out for the dust cases in 2010. It was found that spatial distributions of $PM_{10}$ calculated by visibility are in good agreement with the observed $PM_{10}$ distribution, especially for the strong dust cases in 2010. And correlation between the derived and observed $PM_{10}$ concentration was 0.63. We applied the function to obtain distributions of $PM_{10}$ concentration over North Korea, in which concentration data are not available, and compared them with satellite derived dust index, IODI distributions for dust cases in 2010. It is shown that the visibility function estimates quite similar patterns of dust concentration with IODI image, which suggests that it can contribute for prediction by indentifying transport route of Asian dust.