The Alfven drift turbulence suppression at the plasma edge is suggested as a triggering mechanism for the L to H transition. The stability theory of Alfven drift-waves shows that with increasing plasma pressure the Alfven waves get coupled to electron drift waves and as a consequence the unstable long wavelength perturbations (most important for transport) are suppressed. The instability can be characterised by two significant parameters, i.e. the normalised plasma beta, beta(n), and the normalised collision frequency, nu(n). The resulting turbulent transport coefficient is suppressed when the normalised beta is greater than a critical value, i.e. beta(n)> 1 + nu(n)(2/)3,which depends on the normalised collision frequency nu(n). The transport coefficients change their dependence on plasma parameters at this threshold. Therefore, the possible scenario for the development of the H-mode could be associated with the stabilisation of the electron fluctuation at the plasma edge. The Alfven drift-wave model predicts the experimental trend of a roughly linear dependence of threshold temperature on magnetic field, with a weak dependence on density at high densities and a strong dependence on density at lower densities.