  FN Tau is a rare example of very low-mass T Tauri stars that exhibits a
spatially resolved nebulosity in near-infrared scattering light. To directly
derive the parameters of a circumstellar disk around FN Tau, observations of
dust continuum emission at 340 GHz are carried out with the Submillimeter Array
(SMA). A point-like dust continuum emission was detected with a synthesized
beam of ~ 0.7" in FWHM. From the analysis of the visibility plot, the radius of
the emission is estimated to be <= 0.29", corresponding to 41 AU. This is much
smaller than the radius of the nebulosity, 1.85" for its brighter part at 1.6
micron. The 340 GHz continuum emission observed with the SMA and the
photometric data at lambda <= 70 micron are explained by a power-law disk model
whose outer radius and mass are 41 AU and (0.24 - 5.9) x 10^{-3} M_{sun},
respectively, if the exponent of dust mass opacity (beta) is assumed to be 0-2.
The disk model cannot fully reproduce the flux density at 230 GHz obtained with
the IRAM 30-meter telescope, suggesting that there is another extended "halo"
component that is missed in the SMA observations. By requiring the halo not to
be detected with the SMA, the lower limit to the size of the halo is evaluated
to be between 174 AU and 574 AU, depending on the assumed beta value. The
physical nature of the halo is unclear, but it may be the periphery of a flared
circumstellar disk that is not described well in terms of a power-law disk
model, or a remnant of a protostellar envelope having flattened structure.
