  We study the existence of $x_2$-directional periodic traveling-wave solutions
for the generalized surface quasi-geostrophic (gSQG) equation, known as von
K\'arm\'an vortex street. These solutions are of $C^1$ type, and obtained by
studying a semiliner problem on typical period. By a variational
characterization to solutions, we also show the relation of vortex size,
traveling speed and street width. In particular, the vortices with positive and
negative intensity have equal or unequal scaling size in our construction,
which constitutes the regularization for two kinds of $x_2$-directional
K\'arm\'an point vortex street.
