  We have determined the distance to M33 using single epoch I-band observations
of Cepheids based on HST/WFPC2 images of five fields in M33. Combining the HST
I-band photometry and the periods determined from the ground-based observations
(DIRECT) for 21 Cepheids with log P>0.8 in the sample of 32 Cepheids, we derive
a distance modulus of (m-M)_0=24.52+/-0.14(random)+/-0.13(systematic) for an
adopted total reddening of M33, E(B-V)=0.20+/-0.04 (E(V-I)=0.27+/-0.05) given
by Freedmand et al.(2001), the reddening to the LMC, E(B-V)=0.10, and the
distance to the LMC, (m-M)_0=18.50. If the total reddening to M33 of
E(B-V)=0.10+/-0.09 given by Freedman, Wilson, and Madore(1991) is used, the
Cepheid distance modulus based on the I-band photometry will be increased by
0.20. Metallicity effect on the Cepheid distance to M33 is estimated to be
small, delta(m-M)_Z=0.01 to 0.06, which leads to (m-M)_0=24.53 to 24.58 after
this metallicity effect correction. Using the Wesenheit W_I, an extinction-free
parameter, we derive a similar value,
(m-M)_0=24.52+/-0.15(random)+/-0.11(systematic). These results are in
reasonable agreement with those based on the ground-based multi-epoch BVRI
observations of brighter Cepheids in M33, and are ~0.3 smaller than those based
on the tip of the red giant branch and the red clump. It is needed to estimate
better the reddening to Cepheids in M33.
