  We construct a finite time blow up solution for the nonlinear Schr\"odinger
equation with the power nonlinearity whose coefficient is complex number. We
generalize the range of both the power and the complex coefficient for the
result of Cazenave, Martel and Zhao \cite{CMZ}. As a bonus, we may consider the
space dimension $5$. We show a sequence of solutions closes to the blow up
profile which is a blow up solution of ODE. We apply the Aubin-Lions lemma for
the compactness argument for its convergence.
