  A gradient flow equation for $\lambda\phi^{4}$ theory in $D=4$ is formulated.
In this scheme the gradient flow equation is written in terms of the
renormalized probe variable $\Phi(t,x)$ and renormalized parameters $m^{2}$ and
$\lambda$ in a manner analogous to the higher derivative regularization. No
extra divergence is induced in the interaction of the probe variable
$\Phi(t,x)$ and the 4-dimensional dynamical variable $\phi(x)$ which is defined
in renormalized perturbation theory. The finiteness to all orders in
perturbation theory is established by power counting argument in the context of
$D+1$ dimensional field theory. This illustrates that one can formulate the
gradient flow for the simple but important $\lambda\phi^{4}$ theory in addition
to the well-known Yang-Mills flow, and it shows the generality of the gradient
flow for a wider class of field theory.
