The anisotropic instability of Alfven waves in solar atmosphere is considered. It is shown that such mechanism leads to the generation not only Alfven, but also kinetic Alfven waves, which is very important in the investigation of processes of heating and particle acceleration in chromospheric and coronal plasma. The criterion of instability development is found. We analyse the conditions under which the given instability can arise and the atmosphere areas in which the origin of the instability is most probable. It is shown that such mechanism of kinetic Alfven wave generation is very effective and can play an essential role in some processes in the solar atmosphere.