Mixed anxiety and depression is common among older adults. The aim of the study was to compare the effects of an eight-week-long tailored internet-supported cognitive behaviour therapy (ICBT) programme and to compare against the provision of weekly general support. A second aim was to investigate if pre-treatment cognitive flexibility and self-reported cognitive problems would predict outcome. We included 66 older adults (aged over 60 years) with mixed anxiety/depression following media recruitment and randomised them into treatment and control groups. We also included a one-year follow-up. As a measure of executive function, we used the Wisconsin Card Sorting Test (perseverative errors) and the Cognitive Failures Questionnaire during the pre-treatment phase. Results showed a moderate between-group effect on the main outcome measure, the Beck Anxiety Inventory (BAI) (d= .50), favouring the treatment group. Nearly half (45.5%) of that group were classified as responders. One person (3%) in the treatment group deteriorated. There were significant correlations between perseverative errors and outcome (on the BAI r = -.45), but not among self-reported cognitive function. We conclude that guided, tailored ICBT may be effective for some older adults and that the role of cognitive function needs to be investigated further.