At ambient pressure, CrAs undergoes a first-order transition into a double-helical magnetic state at TN=265  K, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of the coupled structural/helimagnetic order in this system. Here, we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure (P), that the combined order is suppressed at Pc≈10  kbar, near which bulk superconductivity develops with a maximal transition temperature Tc≈2  K. We further show that the coupled order is also completely suppressed by phosphorus doping in CrAs1−xPx at a critical xc≈0.05, above which inelastic neutron scattering evidenced persistent antiferromagnetic correlations, providing a possible link between magnetism and superconductivity. In line with the presence of antiferromagnetic fluctuations near Pc(xc), the A coefficient of the quadratic temperature dependence of resistivity exhibits a dramatic enhancement as P (x) approaches Pc(xc), around which ρ(T) has a non-Fermi-liquid form. Accordingly, the electronic specific-heat coefficient of CrAs1−xPx peaks around xc. These properties provide clear evidence for quantum criticality, which we interpret as originating from a nearly second-order helimagnetic quantum phase transition that is concomitant with a first-order structural transition. Our findings in CrAs highlight the distinct characteristics of quantum criticality in bad metals, thereby bringing out new insights into the physics of unconventional superconductivity such as those occurring in the high-Tc iron pnictides.