We fabricated thin $L 1_{0}$ -Fe x Pt100– x ( $x = 46$ –54 at.%) polycrystalline perpendicular films, and examined the $x$ dependences of the first- and second-order uniaxial magnetic anisotropy, $K_{u1}$ and $K_{u2}$ , in relation to variant formation. The values of $K_{u1}$ and $K_{u2}$ were estimated from magnetic torque curves at an applied field of 70 kOe obtained using anomalous Hall effect. $K_{u1}$ for films with thickness $d$ of 10 nm showed a maximum at $x = 50$ at.%, which was consistent with the behavior of the order parameter. $K_{u1}$ decreased markedly as $x$ increased from 50 at.%, accompanied by an increase of $K_{u2}$ . In-plane X-ray diffraction analysis revealed that the variant formation increased markedly as $x$ increased, especially beyond $x = 50$ at.%. Moreover, the relative lattice strain evaluated using a Williamson–Hall plot increased remarkably. The significant reduction of $K_{u1}$ , accompanied by the enhancement of $K_{u2}$ , was coincident with variant formation. $K_{u1}$ for films with $d = 2$ nm also showed a maximum at $x = 50$ at.%. However, the $K_{u1} \sim x$ relation showed a good symmetry against Fe content variations from 50 at.%. No increase of $K_{u2}$ with increasing $x$ was observed. It is likely that a large tensile stress in the initial film growth, caused by the lattice misfit between FePt and MgO underlayers, suppressed the variant formation in these very thin films.