In this article, we synthesized a Yb3+-doped two-dimensional (2-D) upconverting Tb metal-organic framework (Tb-MOF) (hereinafter referred to as Tb-UCMOF) by a one-step solvothermal method. The synthesized Tb-UCMOF is composed of stacks of 2-D nanosheets with an average width distributed between 250 and 300 nm, and these nanosheets can be exfoliated by a simple liquid ultrasound method. The structural characteristics of this flaky particle accumulation are confirmed by the type IV adsorption-desorption isotherm with a H3-type adsorption hysteresis loop, and the Brunauer-Emmett-Teller surface of Tb-UCMOF is 143.9257 m2·g-1. Tb-UCMOF has characteristic emissions of Tb3+ which are located at 490, 545, 585, and 621 nm under 980 nm excitation. The upconverting luminescence mechanism is attributed to that Yb3+ absorbs multiple photons and transfers the energy to Tb3+, causing its 4f electrons to jump to the excited state, and then the upconverting emissions are obtained when electrons return to the ground state. Since the Tb-UCMOF nanosheets have high dispersibility and an obvious upconverting luminescent signal, we explored their luminescence sensing properties. The luminescence intensity is found to gradually decrease with the addition of Cu2+, the linear range of Cu2+ sensing is 0-1.4 μM, and the detection limit is 0.16 μM. This rapid, highly selective, and sensitive Cu2+ sensing indicates that 2-D upconverting MOF nanosheets have great application prospects in luminescence sensing and also promote the research of 2-D upconverting MOFs with specific recognition for the application of biological and environmental luminescent sensors.