Summary: ``This paper mainly develops the radial symmetry and monotonicity of entire solutions for fractional parabolic equations. To obtain the symmetry and monotonicity of entire solutions, the narrow region principle and maximum principle for antisymmetric functions in [9] [MR4333971] are needed. Furthermore, to circumvent the difficulty from nonlocality for the fractional Laplacian, a fractional parabolic version of the method of moving planes will be adopted.''