Two-dimensional (2D) Xenes of a single type of element can offer fascinating electronic properties, such as massless Dirac fermions for extremely high charge-carrier mobility and topological insulators for dissipationless electron transport. However, the realization of either the massless Dirac fermions or the topological insulator in a same element system via a simple physical method has rarely been reported, which is of great importance for the development of next-generation electronic devices. Here, by using first-principles calculations, we identify that a 2D square tellurium system can be effectively tuned to realize either the massless Dirac fermions or the topological insulator phase. The 2D square tellurium system shows three structural phases via strain effect, i.e., buckled square, buckled rectangular, and planar square phases, which exhibit extraordinary topological properties. There are four anisotropic Dirac points in the buckled square phase, in which the Fermi velocity can be as high as 9.44 x 10(5) m/s. The buckled rectangular phase can behave as a quantum spin Hall insulator with a band gap of 0.24 eV, pointing towards promising applications for room-temperature devices. There also exist nodal lines in buckled square/planar square structures in the non-spin-orbit-coupling case. These findings extend the knowledge on single-layer materials and promote future applications of the 2D tellurium systems.