<p>The Maccari system plays an important role in describing the nonlinear wave phenomena in nonlinear optics, plasma physics and other related physical field. This paper pays attention to construction of the quasi-periodic breathers for the Maccari system by means of the Hirota’s bilinear method and numerical algorithm. The solvable problem of the quasi-periodic breathers is transformed into a problem of solving algebraic equations. These algebraic equations can be transformed into a real system, which can be formulated as a least square problem and solved by the stabilized Levenberg-Marquardt method. Based on the asymptotic analysis, the relationships between quasi-periodic breathers and breathers are strictly established. In addition, the classification and degradation mechanism of quasi-periodic breathers are studied. The dynamic behaviors including periodicity and wavelength of the quasi-periodic breathers are discussed by utilizing an analytical method related to the characteristic line. The results help us better understand the properties of the quasi-periodic breathers.</p>