$Y(Pr)Ba_2Cu_4O_8$ system is one of the most studied high temperature superconductors. Substitution of Pr for Y in this system suppresses $T_c$ and superconductivity finally disappears at a high Pr doping. There are competing theories for the suppression of $T_c$ but systematic experimental results are very rare. In order to find the change in Fermi surface topology which can affect the superconductivity, we have performed angle-resolved photoemission studies on single crystal samples of $YBa_2Cu_4O_8$ and $PrBa_2Cu_4O_8$. While the Fermi surface of $YBa_2Cu_4O_8$ shows a similar topology to those of other cuprates, we observe only 1D like band structures in $PrBa_2Cu_4O_8$. We find no significant differences in the chain band for both samples.