  In this paper we are concerned with the binary contact path process
introduced in \cite{Gri1983} on the lattice $\mathbb{Z}^d$ with $d\geq 3$. Our
main result gives a hydrodynamic limit of the process, which is the solution to
a heat equation. The proof of our result follows the strategy introduced in
\cite{kipnis+landim99} to give hydrodynamic limit of the SEP model with some
details modified since the states of all vertices are not uniformly bounded for
the binary contact path process. In the modifications, the theory of the linear
system introduced in \cite{Lig1985} is utilized.
