It looks similar to Java in this respect:
Public Class Foo
Public Sub New(name As String)
' Do something '
End Sub
Public Sub New(name As String, bar As Integer)
Me.New(name)
' Do something '
End Sub
End Class
Note that you have to use MyBase.New(...) in case you want to call a constructor of a base class. See also VB.NET OOP Part2 – Understanding Constructors.