Summary: IR/UV mixing in noncommutative (NC) field theory is investigated in the Carlson-Carone-Zobin (CCZ) formalism of Lorentz-invariant NC field theory with the assumption that the fields are ‘independent’ of the ‘internal’ coordinates \(\theta^{\mu\nu}\). A new regularization scheme called ‘NC regularization’ is then proposed. This scheme removes the Lorentzinvariant IR singularity by subtraction from the theory. It requires the usual UV limit \(\Lambda\to\infty\) to be accompanied by the commutative limit \(a\to 0\) with \(\Lambda^2a^2\) fixed, where \(a\) is the length parameter in the theory. The new UV limit gives the usual renormalized amplitude of the one-loop self-energy diagram of the \(\phi^3\) model. It is shown that the new regularization is gauge-invariant; the ‘non-transverse’ part of the vacuum polarization in QED is automatically transverse in Lorentz-invariant NCQED, but the two transverse pieces, one of which is already transverse in QED, possess a Lorentz-invariant IR singularity which should be ‘subtracted off’ at zero external momentum squared. This subtraction leads to the same result as the renormalized one obtained by Pauli-Villars-Gupta or dimensional regularizations. Other diagrams with three-point vertices that contribute to the photon self-energy in Lorentz-non-invariant NCQED all vanish due to Lorentz invariance under the assumption adopted, while the tadpole diagram gives a finite contribution to the charge renormalization, which vanishes if \(\Lambda^2a^2\to 0\). Lorentz-invariant NC \(\phi^4\) and scalar Yukawa models are also studied in the one-loop approximation. A comment is made that Lorentz invariance might lead to a decoupling of \(U(1)\) from \(SU(N)\) in NC \(U(N)\) gauge theory.