We have systematically studied physical properties of Ba(Fe0.97Cr0.03)2(As1−xPx)2, where superconductivity in BaFe2(As1−xPx)2 is fully suppressed by just 3% of Cr substitution of Fe. A quantum critical point is revealed at x ∼0.42, where non-Fermi-liquid behaviors similar to those in BaFe2(As1−xPx)2 are observed. Neutron diffraction and inelastic neutron scattering measurements suggest that the quantum critical point is associated with the antiferromagnetic order, which is not of conventional spin-density-wave type as evidenced by the ω/T scaling of spin excitations. On the other hand, no divergence of low-temperature nematic susceptibility is observed when x is decreased to 0.42 from higher doping level, demonstrating that there are no nematic quantum critical fluctuations. Our results suggest that non-Fermi-liquid behaviors in iron-based superconductors can be solely resulted from the antiferromagnetic quantum critical fluctuations, which cast doubts on the role of nematic fluctuations played in the normal-state properties in iron-based superconductors.