Recently, a sequential adaptive learning algorithm has been developed for online constructing belief-rule-based (BRB) systems. This algorithm is based on the assumption that the sampling density function of the inputs of BRB system obeys the uniform distribution. However, in practice, the sample density function is not available and difficult to obtain, and this really limit the applicability of the above method. As such, it is desired to develop an improved algorithm without requirement for the sample density function. In this paper, along the line of the sequential adaptive learning algorithm, we develop an improved evolving BRB learning algorithm based on the belief incomplete criterion. Compared with the current algorithms, a belief rule can be automatically added into the BRB or pruned from the BRB without need of the sample density function. In addition, our algorithm inherits the feature of the BRB, in which only partial input and output information is required. Based on the improved method, a fault prognosis is presented explicitly. In order to verify the effectiveness of our algorithm, a practical case study for gyroscope fault prognosis is studied and examined to demonstrate how our algorithm can be implemented.