In this paper we investigate the behaviour of the weighted maximal operators of Marcinkiewicz type (C,α)-means σα,∗p ( f ) := supn∈P |σαn ( f )| n2/p−(2+α) in the Hardy space Hp(G 2) (0 < α < 1 and p < 2/(2 + α)). It is showed that the maximal operators σα,∗p ( f ) are bounded from the dyadic Hardy space Hp(G2) to the Lebesgue space Lp(G2), and that this is in a sense sharp. It was also proved a strong convergence theorem for the Marcinkiewicz type (C, α) means of Walsh-Fourier series in Hp(G2).