Galileo has provided initial services since December 2016. Until June 2018, there are 22 satellites in orbit, 15 of which provide normal service while 7 of which are in orbit test. With the improvement of Galileo, there are lots of applications that require precise real-time satellites orbit and clock products. Usually real time satellite clock offsets is calculated based on observations from real time data stream, which is heavily affected by the quality of internet. For some stations or users, data packet loss and data stream interruption occurs frequently. Thus both the generation and access of precise satellite clocks based on real-time data stream are quite challenging. Galileo satellites are equipped with high performance hydrogen atomic clocks, which have better short-term prediction accuracy. Instead of real-time data stream, data from connection of short-arc observation files, like hourly or high-rate files, are used to produce real-time satellites clock in this contribution. Clocks are estimated using 24-hour arc observations and predicted with 2 hours. Experiment results show that this method could improve the reliability of the Galileo real-time clock product.