Summary: In this paper we investigate the compact operators under Orlicz function, named noncommutative Orlicz sequence space (denoted by \(S_\varphi (\mathcal{H}))\), where \(\mathcal{H}\) is a complex, separable Hilbert space. We will show that the space generalizes the Schatten classes \(S_p(\mathcal{H})\) and the classical Orlicz sequence space respectively. After getting some relations of trace and norm, we will give some operator inequalities, such as Holder inequality and some other classical operator inequalities. Also we will give the dual space and reflexivity of \(S_\varphi (\mathcal{H})\) which generalizes the results of \(S_\varphi (\mathcal{H})\). Finally, as an application, we will show that the Toeplitz operator \(T_{1 - \left| z \right|^2}\) on the Bergman space \(L_\alpha^2\left(\mathbb{R} \right)\) belongs to some \(S_\varphi (\mathcal{H})\), and the norm satisfies \(1 = \sum\limits_{n\geq 0}\varphi\left(\frac{1}{(n+2)\Vert T_{1-|z|^2} \Vert_\varphi}\right) \). Especially, if \(\varphi (T) = |T |^p\), \(p > 1\), the norm is \(\Vert T_{1-|z|^2}\Vert_p = \bigg[\sum_{n\geq 0}\frac{1}{(n+2)^p}\bigg]^{\frac 1p} = (\zeta(p) - 1)^{\frac 1p} \), where \(\zeta (p)\) is the Riemann function.