The present invention relates to a process for manufacturing neohexene, comprising contacting isobutene with a supported catalyst comprising a tungsten compound chosen from tungsten hydrides, organometallic tungsten compounds and organometallic tungsten hydrides, and a support comprising an oxide of aluminium, so as to form a reaction mixture comprising neohexene, and preferably separating neohexene from the reaction mixture, so as to isolate it. The contacting leads to the direct production of neohexene, in particular in a single (reaction) stage and with a high molar selectivity for neohexene. The contacting can be performed at a temperature of 50 to 600 °C, under a total absolute pressure of 0.01 to 100 MPa.