In open publications the results of research on the third harmonic generation in the air by femtosecond laser radiation are presented. Most of the studies have been carried out using a titanium-sapphire laser with a central emission wavelength of 800 nm. This work presents for the first time the results of studies of the third harmonic generation in the air from laser radiation with a wavelength of 1032 nm. The source of the laser radiation was an ytterbium femtosecond laser which generated pulses with duration of ~ 250 fs and a repetition rate of 1 kHz. The average output power of the laser reached 1750 mW. Maximum peak intensity of excitation laser radiation was up to 10 TW/cm2. When focusing the laser radiation its filamentation took place and was accompanied by generation of the third harmonic radiation at wavelength of 344 nm. Spectral, energy and spatial characteristics of the generated third harmonic radiation were investigated. Energy measurements were carried out up to the threshold power of pump radiation at which the competing nonlinear processes in the circuit optical elements of the experimental setup began to occur. The maximum average third harmonic emission power was 1.52 mW with a third harmonic conversion efficiency of about 0.085 %. The far-field beam pattern had a symmetric Gaussian profile with a radiation divergence of 0.11 mrad which corresponds to the diffraction quality of the beam (M2 ≈ 1)