A time-differential Brillouin optical correlation domain analysis (BOCDA) sensing system is proposed and demonstrated. The system uses only the zeroth-order correlation peak for Brillouin gain generation between the pump and probe. The pump and probe are individually phase-modulated by two pseudo-random binary sequences which are the same except for bit-delayed relation. Hence, the system does not need an optical delay for selecting the order of the correlation peak, unlike previous BOCDA systems with either phase or frequency modulation. It removes sensing position drift caused by a delay line in the BOCDA system under temperature change. Also, a single spatial resolution is used throughout the sensing fiber length and this resolution can be freely changed for fine or coarse measurement at a specific fiber section without changing the measurement system configuration.