InAs1-x Sb x nanowires show promise for use in nanoelectronics, infrared optoelectronics and topological quantum computation. Such applications require a high degree of growth control over the growth direction, crystal quality and morphology of the nanowires. Here, we report on the silver-assisted growth of InAs1-x Sb x nanowires by molecular-beam epitaxy for the first time. We find that the growth parameters including growth temperature, indium flux and substrate play an important role in nanowire growth. Relatively high growth temperatures and low indium fluxes can suppress the growth of non-[111]-oriented nanowires on Si (111) substrates. Vertically aligned InAs1-x Sb x nanowires with high aspect ratios can be achieved on GaAs (111)B substrates. Detailed structural studies suggest that high-quality InAs1-x Sb x nanowires can be obtained by increasing antimony content. Silver-indium alloy segregation is found in ternary alloy InAs1-x Sb x nanowires, and it plays a key role in morphological evolution of the nanowires. Our work provides useful insights into the controllable growth of high-quality III-V semiconductor nanowires.