In this paper we study some properties of a totally $\ast $-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally $\ast $-paranormal operator. Also we show that Weyl’s theorem and the spectral mapping theorem hold for totally $\ast $-paranormal operators through the local spectral theory. Finally, we show that every totally $\ast $-paranormal operator satisfies an analogue of the single valued extension property for $W^{2}(D,H)$ and some of totally $\ast $-paranormal operators have scalar extensions.