We propose a novel heterogeneous nineteen-core four-mode fiber. The heterogeneous core arrangement and trench-assisted structure can significantly suppress inter-core crosstalk (XT). In order to control the number of modes in the core, a low refractive index area is introduced in the core. The number of LP modes and the effective refractive index difference (Δneff) of adjacent modes in the core are controlled by changing the refractive index distribution of the core and the parameters of the low refractive index area in the core. And the mode state of low intra-core crosstalk is successfully realized in the graded index core. After the optimization of fiber parameters, each core can stably transmit four LP modes under the optimal fiber parameters, and the inter-core crosstalk of LP02 mode is less than -60 dB/km. Finally, the effective mode area (Aeff) and dispersion (D) of nineteen-core four-mode fiber in C+L band are described. The results show that the nineteen-core four-mode fiber is suitable for terrestrial and undersea communication systems, data centers, optical sensors and other fields.