An example of achromatic designs for a negative-refractive-index plane-concave lens with 100 mm focal length, 20 mm the pupil diameter and negative abbe number in near infrared wave band from 0.848 μm to 1.114 μm was given to explain two achromatic methods about the negative-refractive-index lens.The two methods are combing positive-refractive-index lens with negative-refractive-index lens and introducing the diffractive optical elements into the negative-refractive-index lens.The analysis results show that the positive-refractive-index lens undertakes almost all the power in the method of combing positive-refractive-index lens with negative-refractive-index lens, so a large number of additional monochromatic aberrations are introduced.However, the diffraction optical element can correct the chromatic-aberration of the negative-refractive-index lens without introducing additional aberrations.The diffraction efficiency of the negative-refractive-index diffractive optical elements is deduced based on the special propagating laws and imaging properties of negative-index lenses, the expression for microstructure height is given, and the diffraction efficiencies are calculated.The diffraction efficiency for the negative-index binary diffractive optical element in the design wavelength 0.912 μm is 40.53%, in wavelength 0.848 μm is 35.06%, and in wavelength 1.114 μm is 39.83%.