  We investigate the instability toward a skyrmion crystal under an in-plane
magnetic field in centrosymmetric tetragonal magnets. By performing the
simulated annealing for a spin model on the square lattice, we find that the
interplay among the easy-plane two-spin anisotropic interaction, positive
biquadratic interaction, and high-harmonic wave-vector interaction plays an
important role in stabilizing the skyrmion crystal in the in-plane external
magnetic field. The obtained skyrmion crystal consists of a pair of vortex and
antivortex with opposite polarization in terms of the out-of-plane spin
component. We also show that various multiple-$Q$ states emerge depending on
the model parameters. Our results indicate the possibility of topological spin
textures in centrosymmetric tetragonal magnets with easy-plane magnetic
anisotropy when the ground-state spin configuration at zero field is
characterized by a single-$Q$ in-plane cycloidal spiral state.
