  It is known that, in the noncommutative Schwarzschild black hole spacetime,
the point-like object is replaced by the smeared object, whose mass density is
described by a Gaussian distribution of minimal width $\sqrt{\theta}$ with
$\theta$ the noncommutative parameter. The elimination of the point-like
structures makes it quite different from the conventional Schwarzschild black
hole. In this paper, we mainly investigate the area spectrum and entropy
spectrum for the noncommutative Schwarzschild black hole with $0\leq \theta\leq
(\frac{M}{1.90412})^{2}$. By the use of the new physical interpretation of the
quasinormal modes of black holes presented by Maggiore, we obtain the quantized
area spectrum and entropy spectrum with the modified Hod's and Kunstatter's
methods, respectively. The results show that: (1) The area spectrum and entropy
spectrum are discrete. (2) The spectrum spacings are dependent on the parameter
$\frac{M}{\sqrt{\theta}}$. (3) The spacing of the area spectrum of the
noncommutative Schwarzschild black hole is smaller than that of the
conventional one. So does the spacing of the entropy spectrum. (4) The spectra
from the two methods are consistent with each other.
