您从未将连接字符串分配给连接对象，就像错误所说。

在con.open之前插入一行设置连接字符串。

  Con.connectionstring = connection 
 Con.Open（）
 

使用语句如下

  Dim Connection As String =Data Source = .\SQLEXPRESS; AttachDbFilename = G：\VB Project \ Library Catalog System \Library Catalog System \library.mdf;集成
 Security = True; Connect Timeout = 30;用户实例= True

使用Con As新的SqlConnection ）
 

Every time I tried to connect to the database it give me this error "The ConnectionString property has not been initialized"

what can I do to solve this?

here are my codes

Module Module1
    Function GetInfoForStudent(ByRef QueryName As String, ByVal UserName As String, ByVal Password As String) As DataTable
        Using Con As New SqlConnection
            Try
                Using OleCon As New SqlConnection
                    Dim Connection As String = "Data Source=.\SQLEXPRESS;AttachDbFilename=G:\VB Project\Library
Catalog System\Library Catalog System\library.mdf;Integrated
Security=True;Connect Timeout=30;User Instance=True"
                    Con.Open()
                    Dim Cmd As SqlCommand = Con.CreateCommand()
                    Cmd.CommandType = CommandType.StoredProcedure
                    Cmd.CommandText = QueryName
                    Cmd.Parameters.AddWithValue("@user", UserName)
                    Cmd.Parameters.AddWithValue("@pass", Password)
                    Dim da As New SqlDataAdapter(Cmd)
                    Dim ds As New DataTable()
                    da.Fill(ds)
                    Return ds
                End Using
            Catch ex As Exception

                Throw New Exception(ex.Message)
            End Try
        End Using

    End Function

End Module

Sub ShowStudentInfo()
    Dim dt As DataTable = GetInfoForStudent("MyStoredProcName", "@user", "@pass")
    ' Since (presumably) only one is returned
    With dt.Rows(0)
        ' Assign your text boxes 
        StudentIDTextBox.Text = .Item("StudentID")
        LoginIDTextBox.Text = .Item("LoginID")
        Student_NameTextBox.Text = .Item("Student Name")
        Student_addressTextBox.Text = .Item("Student address")

    End With
End Sub

You never assigned your connection string to the connection object, just like the error is saying.

Insert a line setting the connection string before con.open.

Con.connectionstring = connection
Con.Open()

Or better yet, change your using statement as follows

Dim Connection As String = "Data Source=.\SQLEXPRESS;AttachDbFilename=G:\VB Project\Library Catalog System\Library Catalog System\library.mdf;Integrated
Security=True;Connect Timeout=30;User Instance=True"

Using Con As New SqlConnection(connection)