This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input-output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input-output data are non-negative or not. It successfully addresses the infeasibility issue of both the conventional radial super-efficiency DEA model and the Nerlove-Luenberger super-efficiency DEA model under the assumption of variable returns to scale. Moreover, it can project each DMU onto the super-efficiency frontier along a suitable direction and never leads to worse target inputs or outputs than the original ones for inefficient DMUs. Additional advantages of the proposed model include monotonicity, units-invariance and translation-invariance. Two numerical examples demonstrate the practicality and superiority of the new model.