  Compact protoplanetary disks with a radius of $\lesssim$ 50 au are common
around young low-mass stars. We report high resolution ALMA dust continuum
observations toward a compact disk around CW Tau at Band 4 ($\lambda=2.2$ mm),
6 (1.3 mm), 7 (0.89 mm) and 8 (0.75 mm). The SED shows the spectral slope of
$2.0\pm0.24$ between 0.75 and 1.3 mm, while it is $3.7\pm0.29$ between 2.17 and
3.56 mm. The steep slope between 2.17 and 3.56 mm is consistent with that of
optically thin emission from small grains ($\lesssim$ 350 ${\rm \mu m}$). We
perform parametric fitting of the ALMA data to characterize the dust disk.
Interestingly, if the dust-to-gas mass ratio is 0.01, the Toomre's Q parameter
reaches $\sim$ 1-3, suggesting that the CW Tau disk might be marginally
gravitationally unstable. The total dust mass is estimated as
$\sim250M_{\oplus}$ for the maximum dust size of 140 ${\rm \mu m}$ that is
inferred from the previous Band 7 polarimetric observation and at least
$80M_{\oplus}$ even for larger grain sizes. This result shows that the CW Tau
disk is quite massive in spite of its smallness. Furthermore, we clearly
identify a gap structure located at $\sim20$ au, which might be induced by a
giant planet. In spite of these interesting characteristics, the CW Tau disk
has normal disk luminosity, size and spectral index at ALMA Band 6, which could
be a clue to the mass budget problem in Class II disks.
