The phrase "complete a course" is correct and usable in written English.
It implies that someone has finished a course of study or a program. For example: I'm proud to say that I have completed a course in French language.
Soon we'll be hearing about the "dramatic rise" in MOOC completion rates, without a mention of how much easier it is to complete a course.
She also had to complete a course on the finances of homeownership.
The airline issues certificates to passengers who successfully complete a course.
First the students complete a course in basic skills, followed by a minimum volunteering requirement.
Law students who take part in the program must complete a course in domestic violence advocacy offered by the center.
AR.Race 2 runs on iPhones and iPads, and operates as a racing game for the drone, with players taking turns to complete a course as quickly as possible.
In Britain the first women to complete a course claim to have seen their breasts increase by up to three cup sizes.
Every 18 months they must complete a course established at Fort Bragg called Advanced Urban Combat -- that is, the storming of buildings.
Sandra, who suffers drug and alcohol problems, recently had the children in her photograph taken into care until she can complete a course of rehab.
Doctors, who rarely have more than a few minutes to attend to the very sick, are grateful when they see that their patients eat better, sleep better and are better able to complete a course of therapy, she added.
An exploratory promotional trip to England in 1979 was extended to enable Dread to complete a course at the National Broadcasting School in London and support the Clash on a round-Britain tour early in 1980.
