Detailed observations of larval Drosophila chemotaxis have characterised the relationship between the odour gradient and the runs, head casts and turns made by the animal. We use a computational model to test whether hypothesised sensorimotor control mechanisms are sufficient to account for larval behaviour. The model combines three mechanisms based on simple transformations of the recent history of odour intensity at the head location. The first is an increased probability of terminating runs in response to gradually decreasing concentration, the second an increased probability of terminating head casts in response to rapidly increasing concentration, and the third a biasing of run directions up concentration gradients through modulation of small head casts. We show that this model can be tuned to produce behavioural statistics comparable to those reported for the larva, and that this tuning results in similar chemotaxis performance to the larva. We demonstrate that each mechanism can enable odour approach but the combination of mechanisms is most effective, and investigate how these low-level control mechanisms relate to behavioural measures such as the preference indices used to investigate larval learning behaviour in group assays.