This article is concerned with a class of continuous-time Markovian jump linear systems where the regime transition rates are determined through an initial policy. The purpose is to study the jump linear quadratic regulator for such class of systems. A two-level regulating method is adopted to design the state-feedback controller and the policy separately. The problem of tuning the existing policy with respect to a prescribed quadratic performance criterion is formulated as a gradient projection-based iterative optimisation. This method leads to a near-optimal policy whose performance is better than that of the initial one. Useful characteristics of such a policy are also developed. The efficiency of the main results is elucidated by two numerical examples.