Animal movement can be significantly altered in human‐dominated landscapes such as urban and peri‐urban areas, where habitat is often fragmented and/or linear. Knowledge regarding how wildlife respond to anthropogenic change is vital for informing conservation efforts in such landscapes, including the design of nature reserves and wildlife corridors. To better understand how threatened species persist and behave within human‐dominated landscapes, we examined the home range and space use of the nationally endangered southern brown bandicoot Isoodon obesulus obesulus in peri‐urban Melbourne, Australia’s second‐largest city. Specifically, we examined whether: (1) bandicoots were confined to linear strips of remnant vegetation or also made use of the broader highly modified landscape matrix; (2) the configuration of the linear vegetated strips affected home range shape; and (3) home range area differed between bandicoots living in linear strips and those in larger remnant habitat patches. We found that: (1) 71% of adult males and 33% of adult females used the matrix, but non‐dispersing juveniles were entirely confined to the linear strips; males also travelled greater distances into the matrix (away from the vegetated strips) than females; (2) bandicoots had longer home ranges in narrower strips and males had longer home ranges than females; and (3) home range area for both sexes was smaller in linear strips than has been recorded in other studies in larger remnant habitats. Our study highlights the importance of retaining narrow, fragmented and modified vegetation to accommodate threatened biodiversity within human‐dominated landscapes, but suggests the surrounding matrix may also offer important resources for adaptable species, such as bandicoots. Supporting off‐reserve conservation of biodiversity in novel ecosystems is increasingly pertinent in our rapidly urbanizing world.