In recent years, mathemacians ([1], [3], [5], [22], [23]) introduced and investigated the Fubini Apostol-type numbers and polynomials. They gave some recurrence relations explicit properties and identities for these polynomials. In [12], author considered unified degenerate Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials and gave some relations and identities for these polynomials. In this article, we consider a parametric unified Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials. By using the monomiality principle, we give some relations for the parametric unified Apostol-type Bernoulli, Euler, Genocchi and Fubini polynomials. Furthermore, we give summation formula for these polynomials.