  In this paper, we propose a fast proximal gradient algorithm for
multiobjective optimization, it is proved that the convergence rate of the
accelerated algorithm for multiobjective optimization developed by Tanabe et
al. can be improved from $O(1/k^2)$ to $o(1/k^2)$ by introducing different
extrapolation term $\frac{k-1}{k+\alpha-1}$ with $\alpha>3$. Further, we
establish the inexact version of the proposed algorithm when the error term is
additive, which owns the same convergence rate.
  At last, the efficiency of the proposed algorithm is verified on some
numerical experiments.
