A high precision fused silica differential dilatometer has been developed with a basis on a TMA (Thermo-Mechanical Analyser) in order to measure the linear thermal expansion coefficient (LTEC) of solids in the temperature range of 20 to 400K with total uncertainties of 10nm and 50mK in length and temperature, respectively. To improve the performance of the measurement system, the sensitivity of LVDT (Linear variable differential transformer) is absolutely determined by using a laser interferometer, the temperature of LVDT system is highly stabilized to minimize the zero point drift of the system, and the temperature of the specimen is accurately measured by a combination of a calibrated PRT (Platinum resistance thermometer) and a differential AuFe-Chromel thermocouple. LTECs were measured under a constant heat/cool mode to improve the measurement efficiency. An error analysis shows that the length and temperature measurements under such a nonequilibrium condition maintain the same accuracy as the measurements under the equilibrium condition. The performance of the apparatus was evaluated by measuring copper (SRM 736) and tungsten (SRM 737) certified by NIST (National Institute of Standards and Technology). The present data of LTEC agree with the NIST reference values within 0.1×10-6/K on both specimens.