The truncatedq-Bernstein polynomialsBn,m,qf;x,n∈ℕ, and m∈ℕ0emerge naturally when theq-Bernstein polynomials of functions vanishing in some neighbourhood of 0 are considered. In this paper, the convergence of the truncatedq-polynomials on0,1is studied. To support the theoretical results, some numerical examples are provided.