A procedure for synthesizing a three-dimensional earthquake ground motion to be used for aseismatic structural design is presented. This paper proposes that the synthesized ground motion can be obtained as output sequence of dynamical system having an appropriate pulse-transfer-function under inputting a required innovation process to the system. Sections of this paper are as follows; 1. Introduction 2. Dynamical system generating the simulated earthquake ground motion 3. Stochastic difference equation for the dynamical system 4. Earthquake-engineering meanings of pulse-transfer-function and innovation process 5. Generation of synthesized earthquake ground motion 6. Earthquake records used for studies 7. Pulse-transfer-function expressing information on observation site 8. Innovation variances expressing information on epicenter and earthquake transmission 9. Example of synthesized earthquake ground motion 10. Conclusion