  Algebraic dichotomy is a generalization of an exponential dichotomy (Lin,
JDE2009). This paper gives a version of Hartman-Grobman linearization theorem
assuming that linear system admits an algebraic dichotomy, which generalizes
the Palmer's linearization theorem. Besides, we prove that the homeomorphism in
the linearization theorem (and has a H\"{o}lder continuous inverse). Comparing
with exponential dichotomy, algebraic dichotomy is more complicate. The
exponential dichotomy leads to the estimates
$\int_{-\infty}^{t}e^{-\alpha(t-s)}ds$ and
$\int_{t}^{+\infty}e^{-\alpha(s-t)}ds$ which are convergent. However, the
algebraic dichotomy will leads us to
$\int_{-\infty}^{t}\left(\frac{\mu(t)}{\mu(s)}\right)^{-\alpha}ds$ or
$\int_{t}^{+\infty}\left(\frac{\mu(s)}{\mu(t)}\right)^{-\alpha}ds$, whose the
convergence is unknown in the sense of Riemann.
