[header] How to train a cat to stop fearing sudden movements [title] Talk with your vet. [step] Before you begin any serious attempts to modify your cat's behavior, make an appointment with the vet to eliminate any possible bodily causes. Your vet will ask you about your cat's history and may request some blood tests as well. 
If your cat has only recently started to exhibit more fear, it is possible that there is a physical explanation, such as thyroid disease. [substeps] Your vet may recommend placing your cat on some anti-anxiety medication.