The ground-state magnetic phase diagram of a two-leg spin ladder with trimerized modulated rung exchange is studied using the continuum-limit bosonization approach. In the limit where the rung exchange is dominant, the model is mapped onto the effective quantum sine-Gordon model with topological term. Six quantum phase transitions at different critical magnetic fields are identified. We have shown that the magnetization curve of the system exhibits two plateaus at magnetization equal to the 1/3 and 2/3 of the saturation value. The width of the plateaus, is proportional to the excitation gap at given magnetization and scales as , where is the amplitude of rung-exchange modulation and the critical exponent is obtained as in the case of a ladder with antiferromagnetic legs and in the case of ladder with ferromagnetic legs.