We introduce the notion of a near left almost ring (abbreviated as nLA-ring) which is in fact a generalization of left almost ring. A near left almost ring is a non-associative structure with respect to both the binary operations "+" and ".". However, it possesses properties which we usually encounter in "near ring" and "LA-ring". Historically, the first step towards the near-rings in axiomatic research was done by Dickson in 1905. He showed that there do exist, "Fields" with only one distributive law" (Near-fields) some year later these near-fields showed up the connection between near-field’s and fixed-point free permutation groups. A couple of years later Veblen and Wedderburn started to use near-field’s coordinatize certain kinds of geometric planes.