The invention provides a current initial traveling wave detection apparatus and a transformer station outgoing line cable fault monitoring method. The current initial travelling wave detection apparatus includes a current transformer. The current transformer is connected to a first lead wire and a second lead wire. The first lead wire and the second lead wire are provided with a first circuit breaker thereon. The first lead wire is connected to a first electrically conductive seat. The first electrically conductive seat and a second electrically conductive seat are provided with a second circuit breaker therebetween. The transformer station outgoing cable fault monitoring method includes the following steps: acquiring the initial travelling wave of a three-phase current of respective lines, analyzing the current initial travelling wave, and determining a fault line. According to the invention, the technical solution, compared with prior art, has the following advantages that: can provide an appropriate current transformer based on on-site requirements, is easy to install and use, can determine a fault line based on the contrary polarities of a transient zero module current initialtraveling wave of a fault line and a non-fault line, and is very reliable.