The ferromagnetic resonance (FMR) spectra of an yttrium‐iron‐garnet (YIG) film were studied from room temperature to 120 K above TC (TC = 553 K). The spectra were measured for a magnetic field parallel to the film as well as perpendicular to it. In the ferromagnetic phase the FMR lines represent the magnetostatic modes whose field positions and spacing are determined by the magnetization of the sample. When anisotropy terms are added to the theoretical expressions for magnetostatic waves of Damon and van de Vaart [J. Appl. Phys. 36, 3453 (1965)] for the perpendicular orientation and of Damon and Eshbach [J. Phys. Chem. Solids 19, 308 (1961)] for the parallel one, a good agreement is obtained between the experimental results and theory. Magnetization values extracted from the FMR spectra are also in good agreement with the published magnetization data for YIG, obtained by a vibrating sample magnetometer. At temperatures higher than 413 K the normalized cubic anisotropy K1/M is found to be practically temperature independent, in contrast with previous studies on YIG spheres which conclude that K1/M → 0 when approaching TC. In the paramagnetic phase we observe an anisotropy in the resonance fields due to the sample shape and the induced magnetization. The linewidths ΔH have also been measured and the product [ΔH - ΔH(TC)] × T is found to be practically linearly dependent on T - TC in a wide range of temperatures. ΔH(TC) is the linewidth at TC. This result is in good agreement with recent experimental studies of paramagnetic YIG linewidths and in fair agreement with Huber’s zero‐field theory of paramagnetic linewidths near TC of non‐Heisenberg ferromagnets, where the ‘‘critical speeding‐up’’ effect is absent [J. Phys. Chem. Solids 36, 723 (19- 75)].