A novel core–shell heterostructure with multi‐walled carbon nanotubes (MWCNTs) as the core and graphene oxide nanoribbons (GONRs) as the shell (MWCNT@GONR) is investigated for the first time as anode material for Na‐ion batteries (NIBs) in this study. The MWCNT@GONR material with carboxylic acid groups has been synthesized through unzipping of MWCNTs by a microwave‐assisted process. The influence of the amount of carboxylic acid groups on the electrochemistry of MWCNT@GONR is investigated in this work by applying thermal treatment at different temperatures. In this MWCNT@GONR core‐shell structure, the MWCNTs between flat GONR sheets prevent the restacking problem of graphene and enable penetration of the electrolyte. MWCNTs provide high electronic conductivity and direct electron transfer path while GONRs provide high surface area and defect sites (carboxylic acid groups, COOH‐) that can adsorb more Na ions on the surface thereby increasing capacity. MWCNT@GONR provides high capacity (317 mA h g⁻¹) at a current density of 50 mA h g⁻¹ in the second cycle. A full cell using MWCNT@GONR as anode and P2‐Na_xMnO₂ as cathode is fabricated and it exhibits a high energy density of 99 Wh kg⁻¹ which successfully demonstrates that MWCNT@GONR is a promising anode material for NIB applications.