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tokens: ) but in the range of the H α -excess galaxies at redshifts ∼4−5 that were recently identified in the Spitzer UltraVISTA ultra-deep stripes survey (SMUVS survey; Caputi et al. 2017 ). An important fraction (15%) of the SMUVS galaxies in the 9.4 ≤ log( M stellar [ M ⊙ ]) ≤ 11.0 mass range appear to be in a starburst phase with SFR of hundreds to thousands M ⊙ yr −1 and sSFR well above 24 Gyr −1 , and up to 120 Gyr −1 . The SMUVS galaxies in the starburst phase account for more than 50% of the cosmic SFR density at redshifts ∼3.9−4.9. Therefore, extreme UV luminous galaxies such as BOSS-EUVLG1 could represent the short lived phase of this class of H α -excess galaxies, and could be important contributors to the SFR density at intermediate and high redshifts. BOSS-EUVLG1, therefore, brings on the opportunity to investigate the presence and properties of ionized gas outflows for the first time in this class of extreme star-forming galaxies. In this article, we report the detection of the ionized phase of the outflow in BOSS-EUVLG1 using the H α emission line. Section 2 describes the observations and calibrations of the H α spectrum. Section 3 presents the analysis of H α emission and rest-frame UV absorption lines. The results of the analysis and interpretation as outflowing material are presented in Sect. 4 , including the overall kinematic and mass (Sect. 4.1 ), the outflowing mass rate and mass-loading factor (Sect. 4.2 ), the nature of the energy source (Sect. 4.3 ), and the mass escape fraction into the intergalactic medium (Sect. 4.4 ). The results are discussed in Sect. 5 , focusing in the comparison with low- and high- z SFGs (Sect. 5.1 ), the multi-phase nature of the outflows (Sect. 5.2 ), and the possibility of detecting these outflows with the future X-ray observatory Advanced Telescope for High ENergy Astrophysics (ATHENA; Sect. 5.3 ). Finally, Sect. 6 present the summary and outlook. We adopted H 0 = 67.7 km s −1 Mpc −1 and Ω m = 0.307 ( Planck Collaboration XIII 2016 ) as cosmological parameters and the Salpeter initial mass function (IMF; Salpeter 1955 ) throughout this paper. A factor of 1.66 ( Newman et al. 2012 ) is used to convert the SFRs and stellar masses ( M stellar ) from a Chabrier (2003) to a Salpeter (1955) IMF when using some published data. 2. Observations Near-infrared (Near-IR) long-slit spectroscopy of BOSS-EUVLG1 was obtained with the Espectrógrafo Multiobjeto Infra-Rojo (EMIR) instrument on the 10.4 m Gran Telescopio Canarias (GTC). Observations were taken in two service mode nights – 2020 February 10 and May 8 – in bright Moon and subarcsec seeing (≃0.8′′ full width half maximum) conditions, as part of the GTC program GTCMULTIPLE2E-19A (PI: R. Marques-Chaves). The observations used the K g r i s m with a dispersion of 1.71 Å pix −1 and a 0.8′′-wide long-slit, providing a spectral resolution of 82 km s −1 at ∼2.25 μm. The slit was centered on a bright ( K = 17.43 ± 0.02, AB) reference star (SDSS