The present study is conducted to study a new type convergence, called A-statistical convergence. In the beginning of the study, the concept of infinite, non-negative regular matrices is introduced. Some basic properties of regular and conservative matrices are studied. These matrices play an important role in the theory of A-statistical convergence. Every non-negative regular matrix defines a density function. These density functions are then used to define some new type of convergences such as, statistical convergence, lacunary statistical convergence and lambda statistical convergence. A-statistical convergence is the extension of the other statistical type convergences. Statistical convergence, Lacunary statistical convergence and Lambda statistical convergences can be considered as the special cases of A-statistical convergence produced by different non-negative regular matrices.