We have investigated magnetic field dependences of a ferroelectric incommensurate-helimagnetic order in a trigonal magneto-electric (ME) multiferroic CuFe1−xAlxO2 with x = 0.015, which exhibits the ferroelectric phase as a ground state, by means of neutron diffraction, magnetization and dielectric polarization measurements under magnetic fields applied along various directions. From the present results, we have established the H-T magnetic phase diagrams for the three principal directions of magnetic fields; (i) parallel to the c axis, (ii) parallel to the helical axis, and (iii) perpendicular to the c and the helical axes. While the previous dielectric polarization (P ) measurements on CuFe1−xGaxO2 with x = 0.035 have demonstrated that the magnetic field dependence of the 'magnetic domain structure' results in distinct magnetic field responses of P [S. Seki et al., Phys. Rev. Lett., 103 237601 (2009)], the present study have revealed that the anisotropic magnetic field dependence of the ferroelectric helimagnetic order 'in each magnetic domain' can be also a source of a variety of magnetic field responses of P in CuFe1−xAxO2 systems (A =Al, Ga).