The intersection with special width approach lane (SWAL) is a newly proposed unconventional intersection design. A microscopic traffic flow model was proposed for describing the operation of vehicles at signalised intersections with SWAL. The operation process of driving on the SWAL was divided into four segments, including entering segment, transition segment, special width lane segment, and exiting segment. The car-following and lane selection behaviours of vehicles in these segments are analysed. The parameters used in the model were calibrated using the field data collected in Germany. The proposed model was realised in a time-discretised simulation. The sensitivity analyses of geometric, traffic, and signal factors were conducted. The results show that for the car-following behaviour, the passenger cars on the narrowed lanes cannot drive as efficient as on the normal width lane. For lane selection behaviour, it mainly depends on the distance between the two nearest vehicles in front of the two narrow lanes. The effectiveness of the SWAL depends on whether it is long enough to accommodate the queuing vehicles, which is a combined result of the layout design and the signal timing.