Let H be a complex Hilbert space with inner product ⟨ · , · ⟩ and let A be a non-zero bounded positive linear operator on H. Let BA(H) denote the algebra of all bounded linear operators on H which admit A-adjoint, and let NA(·) be a seminorm on BA(H). The generalized A-numerical radius of T∈ BA(H) is defined as ωNA(T)=supθ∈RNA(eiθT+e-iθT♯A2),where T♯A stands for a distinguished A-adjoint of T. In this article, we focus on the development of several generalized A-numerical radius inequalities. We also develop bounds for the generalized A-numerical radius of sum and product of operators.