The growth of solutions of higher order homogeneous linear differential equation

f

(

+

A

k－1

(z)

P

k－1

(e

z

)f

′

+…+

A

1

(z)

P

1

(e

z

)f

′

+

A

0

(z)

P

0

(e

z

)f=0is investigated

where

A

j

(z)≠0(j=0

1

…

k－1) are entire functions

P

j

(e

z

)(j=0

1

…

k－1) are nonconstant polynomials of e

z

without constant term

and deg

P(

z) is not equal to deg

Q

(z). It is showed that the order of growth of each nonzero solution of the above equations is infinite.