We show that the tethered surface model of Helfrich and Polyakov-Kleinert undergoes a first-order phase transition separating the smooth phase from the crumpled one. The model is investigated by the canonical Monte Carlo simulations on spherical and fixed connectivity surfaces of size up to N = 15 212. The first-order transition is observed when N > 7000, which is larger than those in previous numerical studies, and a continuous transition can also be observed on the smaller surfaces. Our results are therefore consistent with those obtained in previous studies on the phase structure of the model.