Under investigation in this paper is the N-coupled Hirota system which describes the ultrashort pulse simultaneous propagation of the N-field components in an optical fiber. Through the Hirota method and symbolic computation, using some auxiliary functions, we obtain the improved bilinear forms and two mixed-type soliton solutions for the 3-coupled Hirota system, while the system admits two mixed-type solitons for all the cases of sigma(1), sigma(2) and sigma(3), which the represent the defocusing or focusing nonlinearities of the 3 components. With the help the analytic and graphic analysis, we study the properties and interactions for the two mixed-type solitons for the 3-coupled Hirota system. Amplitudes for the two mixed-type one solitons are not affected by gamma, but their velocities are linearly related to gamma, with gamma as the higher-order effect which represents the relative width of the spectrum that arises due to the quasi-monochromocity. For the 2-bright-1-dark two solitons, there exist the elastic and inelastic interactions, while for the 1-bright-2-dark two solitons, there is only the elastic interaction. The 2-bright-1-dark and 1-bright-2 dark bound-state two solitons are also presented. Finally, we extend those results to the N-coupled Hirota system. (C) 2016 Elsevier Ltd. All rights reserved.