A soft Sensor is a model which is used to estimate the unmeasurable output of an industrial process. It is very useful in process control because it can be used to control and monitor many industrial processes. But designing a soft sensor is usually difficult because its modeling is often based on case data. These data have the features of discreteness, nonlinearity, contradiction, and complexity. In this paper, modeling based on case data is defined as a case based modeling problem. In order to solve the case based modeling problem and successfully design a soft sensor, this paper constructs a kind of fuzzy distributed radial basis function neural network. The fuzzy distributed RBF neural network is easy to solve the case based modeling problem. In this paper, it is applied in designing a soft sensor for a high purity distillation column. The simulation is based on the actual operation data and analysis data of the distillation column. The results show that the fuzzy distributed RBF neural network based soft sensor has good performance. Thus, the fuzzy distributed RBF neural network has successfully solved the case based modeling problem. It is very promising in process control.