Optical fibers designed for high power laser radiation delivery represent important tools in medicine, solar systems, or industry. For such purposes several different types of glass optical fibers such as silica, sapphire, or chalcogenide ones as well as hollow-glass fibers, photonic crystal fibers and Bragg fibers have been investigated. Air-core Bragg fibers or photonic crystal fibers offer us the possibility of light transmission in a low dispersive material - air having a high damage threshold and small non-linear coefficient. However, preforms for drawing Bragg fibers can be fabricated by MCVD method similarly as preforms of standard silica fibers. In this paper we present fundamental characteristics of laboratory-designed and fabricated Bragg fibers with air cores intended for delivery of laser radiation at a wavelength range from 0.9 to 1.5 μm. Bragg fibers with different air core diameters of 5, 45 and 73 mm were prepared. The fiber core was surrounded by three pairs of circular Bragg layers. Each pair was composed of one layer with a high and one layer with a low refractive index with a contrast up to 0.03. Several laser sources emitting at 0.975, 1.06, and 1.55 μm were used as radiation sources. Attenuation coefficients, overall transmissions, bending losses, and spatial profiles of output beams from fibers were determined at these wavelengths. The lowest attenuation coefficient of 70 dB/km was determined for the 45 μm and 73 mm air-core fiber when radiation from a laser was launched into the fibers by using optical lenses. However, multimodal transmission has been observed in such condition. It has also been found that bending losses of such fibers are negligible for bending diameters higher than 15 mm.