A quantum correlation NFG,A for (n+m)-mode continuous-variable systems is introduced in terms of local Gaussian unitary operations performed on Subsystem A based on Uhlmann fidelity F. This quantity is a remedy for the local ancilla problem associated with the geometric measurement-induced correlations; is local Gaussian unitary invariant; is non-increasing under any Gaussian quantum channel performed on Subsystem B;and is an entanglement monotone when restricted to pure Gaussian states in the (1+m)-mode case. A concrete formula for (1+1)-mode symmetric squeezed thermal states (SSTSs) is presented. We also compare NFG,A with other quantum correlations in scale, such as Gaussian quantum discord and Gaussian geometric discord, for two-mode SSTSs, which reveals that NFG,A has some advantage in detecting quantum correlations of Gaussian states.