Freezing structures of free silver nanodroplets containing different numbers of atoms have been studied by using MD simulation and adopting quantum Sutton-Chen (QSC) potential. It is demonstrated that during most of the solidification processes there are a first order and a continuous phase transitions. By means of the cluster-type index method (CTIM-2) and three dimension graphic techniques, the internal structures of final nanoparticles have been investigated intensively. Besides regular crystalline, decahedral and icosahedral nanoparticles, some very interesting novelty morphologies have also been found. From geometrical views, these novelty structures can be called surface-isomers, because they can be constructed on the base of regular crystalline, decahedral or icosahedral nanoparticles by adding few layers with specific atomic arrangement. These new morphologies have well global (three- or five-fold) symmetry and lower energy than other structures, with same size and one of them is in agreement with the observation in experiment [Phys. Rev. Lett. 92 (2004) 196102].