Are grades an accurate measure of person's intelligence?

Not necessarily. In fact, this is a very controversial subject. Many people (both educators and parents) do believe that grades are the best way to assess if a student has mastered the course material; but others are not so sure. Since grades are usually determined by tests (whether assessments or exams, or even course work), these measurement tools do not always factor in that some students have test anxiety, or learning disabilities that make it difficult for them to score well on tests, or come from an impoverished background where they lack the most up-to-date learning aides like computers. Also, like anyone, a student might have a bad day and get a poor grade on an exam, even if they did know the material. Of course, there needs to be a way to decide how well students are doing. Many educators have come to believe that tests are one way to measure a student's intelligence, but they are not the only way.

If you are asking about IQ tests specifically, those too are controversial. Many critics believe these tests are biased towards upper-middle and upper-class kids. It is well-documented that children are affected by their environment, especially in the formative years. If they come from homes where the parents are not able to speak English well, or homes where poverty prevents the parents from access to books and computers, the child may not come to school with a good enough vocabulary or reading skills; poor children often get lower scores on tests, including IQ tests. Here too, the need to determine a child's intelligence is certainly understandable, but many kids are grouped into lower-level classes through no fault of their own, rather than because they are not intelligent.