Based on the higher-order nonlinear Schr?dinger equation describing ultrashort pulse transmission in metamaterials, this study presents an exact femtosecond quasi-bright soliton solution and determines its existence conditions by using the traveling wave method. When the group speed dispersion, third-order dispersion, cubic-quintic nonlinearities, self-steepening, and second-order nonlinear dispersion effects are properly balanced, the femtosecond quasi-soliton can exist in nonlinear metamaterials. Without the third-order dispersion and second-order nonlinear dispersion, the soliton in metamaterials can not occur. Based on the Drude model, the existence index regions of the femtosecond quasi-bright soliton are discussed in different nonlinear metamaterials. The results show that femtosecond quasi-soliton can exist in the negative index region of self-defocusing nonlinear metamaterials, and in the positive index region of self-focusing nonlinear metamaterials. Moreover, the intensities and widths of the solitons differ in different regions of the metamaterials, implying that the properties of the formed solitons can be adjusted by choosing different nonlinear metamaterials and different frequencies of the incident wave,making them in the corresponding existence areas.