  We first define Pseudo-Calabi flow, as {equation*}
  {{aligned}{{\partial \varphi}\over {\partial t}}&= -f(\varphi),
\triangle_varphi f(\varphi) &= S(\varphi) - \ul S.{aligned}. \end{equation*}
Then we prove the well-posedness of this flow including the short time
existence, the regularity of the solution and the continuous dependence on the
initial data. Next, we point out that the $L^\infty$ bound on Ricci curvature
is an obstruction to the extension of the pseudo-Calabi flow. Finally, we show
that if there is a cscK metric in its K\"ahler class, then for any initial
potential in a small $C^{2,\alpha}$ neighborhood of it, the pseudo-Calabi flow
must converge exponentially to a nearby cscK metric.
