We present the results of a high resolution (0.27'' px(-1) ) near-infrared H band (1.65 μm) imaging survey of a complete sample of 20 flat spectrum radio quasars (FSRQ) extracted from the 2Jy catalogue of radio sources (Wall & Peacock 1985). The observed objects are intrinsically luminous with median M(B) =3D -25.5. The median redshift of the objects in the sample is z =3D 0.65. At this redshift, the H band observations probe the old stellar population of the hosts at rest frame wavelength of sim1 mum. We are able to detect the host galaxy clearly for six (30 %) FSRQs and marginally for six (30 %) other FSRQs, while the object remains unresolved for eight (40 %) cases. We find the galaxies hosting FSRQs to be very luminous (M(H)sim-27). Compared with the typical galaxy luminosity L* (M*(H)sim-25) they appear sim2 mag brighter, although the undetected hosts may reduce this difference. They are also at least as bright as, and probably by sim1 mag brighter than, the brightest cluster galaxies (M(H)sim-26). The luminosities of the FSRQ hosts are intermediate between host galaxies of low redshift radio-loud quasars and BL Lac objects (M(H)sim-26), and the hosts of high redshift radio-loud quasars (M(H)sim-29), in good agreement with current unified models for radio-loud AGN, taking into account stellar evolution in the elliptical host galaxies. Finally, we find an indicative trend between the host and nuclear luminosity for the most luminous FSRQs, supporting the suggestion based on studies of lower redshift AGN, that there is a minimum host galaxy luminosity which increases linearly with the quasar luminosity. Based on observations collected at the European Southern Observatory, La Silla, Chile. Fig. 1b and the appendix will be found in the on-line version at http://link.springer.de