  In this paper we establish several recurrence relations about Euler-Ap\'ery
type multiple zeta star values and a parametric variant of it by using the
method of iterated integrals. Then using the formulas obtained, we find the
explicit evaluations for some specific Euler-Ap\'ery type multiple zeta star
values and one of its parametric variant, and Euler-Ap\'ery type multiple
$t$-star values.
