Abstract: In this paper, we study the problems on the hyper-order, the e-type order, the dependence relation of solutions for a class of higher order linear differential equations with periodic coefficients, and obtain some relations between e-type order and hyper-order, and precise relations between the two orders and coefficients.In this paper, using e-type order to estimate the growth of solutions of the equations, the estimation is more precise than using the order or the hyper-order.