We present a theoretical study of the magnetic properties for the pyrochlore-like NaCu3F7 compound, which surprisingly experience little or no frustration. The magnetic effective exchange interactions were calculated using ab-initio methods explicitly treating the electronic correlation. A model Hamiltonian (quantum Heisenberg Hamiltonian, and for comparison a spin 1/2 Ising Hamiltonian) was built from these interactions and used to determine the zero temperature magnetic order versus magnetic field. The magnetic order at zero magnetic field is non frustrated and associated with the propagation vector q = ( 0 , 0 , 0 ) . The magnetization versus magnetic field reveals the existence of a 1/3 plateau that could be observed in high-pulsed magnetic field experiments. Analyzing the magnetic interactions, we highlight the importance of the magnetic ion nature, and the lattice distortion, in the non-frustrated nature of the NaCu3F7 magnetic structure, despite its triangular/Kagome subnetworks. We believe that this non-frustrated behavior could also take place in other triangular copper-based systems.