In this article, 3-parameter generalized quaternionic Leonardo p-sequence which is a quaternion generalization of the Leonardo p-sequence is presented. Several properties are examined by means of their homogeneous and non-homogeneous recursive relations. According to the special cases of 3-parameter λ_(i ∈ \{1,2,3\}) and p, all the results given in paper are reducible to all quaternions mentioned in this paper.