  We study the lifespan of solutions for the nonlinear Schr\"odinger equation
id_{t}u+{\Delta}u={\lambda}|u|^{p}, (t,x)\in[0,T)\timesR^{n}, with the initial
condition, where 1<p\leq 1+2/n and {\lambda}\in C. Our main aim in this paper
is to prove an upper bound of the lifespan in the subcritical case 1<p<1+2/n.
