Calculating Average For Each Student And Get The Highest

I want to calculate average of grades of each student and get the highest one with SQL command.

I have 2 tables:

Students:
*StudentId
*StudentName
___________
Grades:
*StudentId
*Grade
___________

I need to calculate average of each student and then get the highest.

My try:

Code:
SELECT Students.StudentId,Students.StudentName,AVG(Grades.Grade) AS avg_grade FROM Students s JOIN Grades g ON Grades.StudentId =Students.StudentId
GROUP BY Students.StudentId, Students.StudentName

ORDER BY avg_grade
LIMIT 1 FROM Students;

I encounter problem with this code, maybe it's Completely wrong...