  We investigate both (pseudo)scalar mesons and diquarks in the presence of
external magnetic field in the framework of the two-flavored
Nambu--Jona-Lasinio (NJL) model, where mesons and diquarks are constructed by
infinite sum of quark-loop chains by using random phase approximation. The
polarization function of the quark-loop is calculated to the leading order of
$1/N_c$ expansion by taking the quark propagator in the Landau level
representation. We systematically investigate the masses behaviors of scalar
$\sigma$ meson, neutral and charged pions as well as the scalar diquarks, with
respect to the magnetic field strength at finite temperature and chemical
potential. It is shown that the numerical results of both neutral and charged
pions are consistent with the lattice QCD simulations. The mass of the charge
neutral pion keeps almost a constant under the magnetic field, which is
preserved by the remnant symmetry of QCD$\times$QED in the vacuum. The mass of
the charge neutral scalar $\sigma$ is around two times quark mass and increases
with the magnetic field due to the magnetic catalysis effect, which is an
typical example showing that the polarized internal quark structure cannot be
neglected when we consider the meson properties under magnetic field. For the
charged particles, the one quark-antiquark loop contribution to the charged
$\pi^{\pm}$ increases essentially with the increase of magnetic fields due to
the magnetic catalysis of the polarized quarks. However, the one quark-quark
loop contribution to the scalar diquark mass is negative comparing with the
point-particle result and the loop effect is small.
