In 1834, Jacobi proved his famous four-square theorem. The sum of four squares can be viewed as an example of the so-called Bell-type quadratic forms, and several authors studied representation number of Bell-type quadratic forms. However, most preceding results are limited to the class number 1 case. In this talk, we derive a closed formula for the representation numbers of each Bell-type quadratic form of class number less than or equal to 2. This is joint work with Chang Heon Kim, Kyoungmin Kim, and Soonhak Kwon.