In this thesis we study the VOAs $V_{mathcal{J},r}$ associated to Hermitian type Jordan algebras $mathcal{J}$. The content of this thesis is divided into three parts. The first part consists of Chapter 1, Chapter 2, and Chapter 3 which give a brief account of the theory of vertex algebras, and the VOA $V_{mathcal{J},r}$ constructed by Ashihara and Miyamoto in cite{AM} when $mathcal{J}$ is the $B$ type Jordan algebra. The second part is from Chapter 4 to Chapter 6. In these chapters we discuss some further properties of the VOA $V_{mathcal{J},r}$ when $mathcal{J}$ is the $B$ type Jordan algebra. In particular we compute the correlation function of generating fields, and we give explicit constructions of the simple quotients $bar{V}_{mathcal{J},r}$ when $rin mathbb{Z}_{neq 0}$ using dual pair type constructions. We also calculate the character formula for the simple quotients $bar{V}_{mathcal{J},r},r=-2n,ngeq 1$. In the third part, in Chapter 7 we sketch the construction of $V_{mathcal{J},r}$ when $mathcal{J}$ is of Hermitian type which include the cases that $mathcal{J}$ is of type $A,B$ and $C$, and we leave some problems for future study.