We demonstrate a simple and practical single-stage ultrafast laser amplifier system that operates at a repetition frequency from 1 to 10 kHz, with millijoule pulse energy and as much as 13 W of average power. The repetition rate can be adjusted continuously from 1 to 10 kHz by new all-solid-state pump laser technology. This is to our knowledge the highest average power ever obtained from a single-stage ultrafast laser amplifier system. This laser will significantly increase the average power and the repetition rate that is easily accessible for high-field experiments such as coherent x-ray generation or for laser-synchrotron studies.