We investigate the growth of meromorphic solutions of homogeneous and nonhomogeneous higher order linear differential equations $$ f^{(k)}+um_{j=1}^{k-1}A_jf^{(j)}+A_0f=0\;\;(k\geqslant 2), $$ $$ f^{(k)}+um_{j=1}^{k-1}A_jf^{(j)}+A_0f=A_k\;\;(k\geqslant 2), $$ where $A_j(z)$ ($j=0,1,\dots,k$) are meromorphic functions with finite order. Under some conditions on the coefficients, we show that all meromorphic solutions $f\not\equiv 0$ of the above equations have an infinite order and infinite lower order. Furthermore, we give some estimates of their hyper-order, exponent and hyper-exponent of convergence of distinct zeros. We improve the results due to Kwon; Chen and Yang; Bela\'{\i}di; Chen; Shen and Xu.