  We investigate the Josephson effect in the graphene nanoribbons of length $L$
smaller than the superconducting coherence length and an arbitrary width $W$.
We find that in contrast to an ordinary superconducting quantum point contact
(SQPC) the critical supercurrent $I_c$ is not quantized for the nanoribbons
with smooth and armchair edges. For a low concentration of the carriers $I_c$
decreases monotonically with lowering $W/L$ and tends to a constant minimum for
a narrow nanoribbon with $W\lesssim L$. The minimum $I_c$ is zero for the
smooth edges but $e\Delta_{0}/\hbar$ for the armchair edges. At higher
concentrations of the carriers this monotonic variation acquires a series of
peaks. Further analysis of the current-phase relation and the Josephson
coupling strength $I_cR_N$ in terms of $W/L$ and the concentration of carriers
revels significant differences with those of an ordinary SQPC. On the other
hand for a zigzag nanoribbon we find that, similar to an ordinary SQPC, $I_c$
is quantized but to the half-integer values $(n+1/2)4e\Delta_{0}/\hbar$.
