Abstract: Trinomial permutation polynomials of the form x^r(ax^2s + bx^s + c) over F_q have been studied where 3|q-1 and s=(q-1)/3. We derive some necessary and sufficient conditions for these trinomials to be permutation polynomials, and construct some examples. Moreover, we discuss the relationship between permutation trinomials of the given type over a tower of finite fields.