The efficacy of vaccines targeting SARS-CoV-2 is becoming apparent now that the mRNA and adenovirus vector vaccines that have been approved for emergency use are showing promise. However, the longevity of the protective immune response and its efficacy against emerging variants remains to be determined. To improve longevity and future protection against variants, we have designed a DNA vaccine encoding both the SARS-CoV-2 spike (S) protein receptor-binding domain (RBD) and its nucleocapsid (N) protein, the latter of which is highly conserved amongst beta coronaviruses. The vaccine elicits strong pro-inflammatory CD4 Th1 and CD8 T-cell responses to both proteins, with these responses being significantly enhanced by fusing the nucleocapsid sequence to a modified Fc domain. We have shown that the vaccine also stimulates high titre antibody responses to RBD which efficiently neutralise in both a pseudotype and live virus neutralisation assay and show cross reactivity with S proteins from the emerging variants Alpha (B.1.1.7) and Beta (B.1.351). This DNA platform can be easily adapted to target variant RBD and N proteins and we show that a vaccine variant encoding the B.1.351 RBD sequence stimulates cross-reactive humoral and T-cell immunity. These data support the translation of this DNA vaccine platform into the clinic, thereby offering a particular advantage for targeting emerging SARS-CoV-2 variants.