Summary: Let \(0<q\le p\le \infty\), \(r\in (0,\infty ]\), and \({\mathcal{M}}^p_{q,r}({\mathbb{R}}^n)\) denote the Bourgain-Morrey space which was introduced by J. Bourgain [Lect. Notes Math. 1469, 179–191 (1991; Zbl 0792.42004)] and has proved important in the study of some linear and nonlinear partial differential equations. In this article, via cleverly combining both the structure of Bourgain-Morrey spaces and the structure of Triebel-Lizorkin spaces and adding an extra exponent \(\tau \in (0,\infty ]\), the authors introduce a new class of function spaces, called Triebel-Lizorkin-Bourgain-Morrey spaces \({\mathcal{M}}{\dot{F}}^{p,\tau }_{q,r}({\mathbb{R}}^n)\). The authors show that \({\mathcal{M}}{\dot{F}}^{p,\tau }_{q,r}({\mathbb{R}}^n)\) is just a bridge connecting Bourgain-Morrey spaces and global Morrey spaces. In addition, by fully using exquisite geometrical properties of cubes of Euclidean spaces, the authors also explore various fundamental real-variable properties of \({\mathcal{M}}{\dot{F}}^{p,\tau }_{q,r}({\mathbb{R}}^n)\) as well as its relations with other Morrey type spaces, such as Besov-Bourgain-Morrey spaces and local Morrey spaces. Finally, via finding an equivalent quasi-norm of Herz spaces and making full use of both the Calderón product and the sparse family of dyadic grids, the authors obtain the sharp boundedness on \({\mathcal{M}}{\dot{F}}^{p,\tau }_{q,r}({\mathbb{R}}^n)\) of classical operators including the Hardy-Littlewood maximal operator, the Calderón-Zygmund operator, and the fractional integral.