We consider the effect of three species of neutrinos with nearly degenerate mass on the cosmic structure formation in a low-matter-density universe within a hierarchical clustering scenario with a flat Gaussian initial perturbation spectrum. The matching condition for fluctuation powers at the COBE scale and at the cluster scale leads to a strong upper limit on neutrino mass. For a flat universe with matter density parameter Omega = 0.3, we obtain m(nu)<0.6 eV for the Hubble constant H0<80 km s(-1) Mpc(-1). Allowing for the more generous parameter space limited by Omega<0.4, H0<80 km s(-1) Mpc(-1) and age t(0)>11.5 Gyr, the limit is 0.9 eV.