The problem of convergence of linear means is considered for the Laguerre-Fourier series of continuous functions. An upper
estimate is obtained for the Laguerre-Lebesgue function in terms of the entries of the matrix which determines the linear
summability method in question. This allows us to prove for such series an analogue of the well-known theorem by S. M. Nikol'skii
which provides necessary and sufficient conditions for the summability of trigonometric Fourier series. A theorem on the
regularity of the summability methods is also established.