Possible N Ω-like dibaryons N Ωccc and N Ω bbb with quantum numbers IJ P = 1 2 2 + are investigated within the framework of quark delocalization color screening model. We find both of these two states are bound, and the binding energy increases as the quarks of the system become heavier. The attraction between N and Ωccc (or Ω bbb ) mainly comes from the kinetic energy term due to quark delocalization and color screening. The effect of the channel-coupling provides more effective attraction to N Ωccc and N Ω bbb systems. Besides, the scattering length, the effective range, and the binding energy, obtained from the calculation of the low-energy scattering phase shifts, also supports the existence of the N Ωccc and N Ω bbb states. All these properties can provide necessary information for experimental search for the N Ω-like dibaryons with heavy quarks. And the experimental progress can also check the mechanism of the intermediate-range attraction of the baryon-baryon interaction in quark models.