  A three-dimensional weak topological insulator (WTI), being equivalent to
stacked layers of two-dimensional quantum spin-Hall insulators, accommodates
massless Dirac electrons on its side surface. A notable feature of WTIs is that
surface states typically consist of two Dirac cones in the reciprocal space. We
study the Landau quantization of Dirac electrons of WTIs in a perpendicular
magnetic field. It is shown that when the magnetic length $l_B$ is much larger
than the interlayer distance $a$, surface electrons are quantized into Landau
levels according to the ordinary quantization rule for Dirac electrons. It is
also shown that, with decreasing $l_B$ toward $a$, each Landau level and its
spin state become modulated in a nontrivial manner. We demonstrate that this is
attributed to the mixing of two Dirac cones induced by the discreteness of the
layered structure.
