  We investigate the multifractals of the normalized first passage time on
one-dimensional small-world network with both reflecting and absorbing
barriers. The multifractals is estimated from the distribution of the
normalized first passage time charactrized by the random walk on the
small-world network with three fractions of edges rewired randomly.
Particularly, our estimate is the fractal dimension D_0 = 0.917, 0.926, 0.930
for lattice points L = 80 and a randomly rewired fraction p = 0.2. The
numerical result is found to disappear multifractal properties in the regime p>
p_c, where p_c is the critical rewired fraction.
