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Shubnikov -de Haas (SdH) oscillations under a dc current bias are experimentally studied on a Hall bar sample of single layer graphene. In dc resistance, the bias current shows the common damping effect on the SdH oscillations and the effect can be well accounted for by an elevated electron temperature that is found to be linearly dependent on the current bias. In differential resistance, a novel phase inversion of the SdH oscillations has been observed with increasing dc bias, namely we observe the oscillation maxima develop into minima and vice versa. Moreover, it is found that the onset biasing current, at which a SdH extremum is about to invert, is linearly dependent on the magnetic field of the SdH extrema. These observations are quantitatively explained with the help of a general SdH formula.The effect of a dc current bias on the nonlinear response of two-dimensional electron systems (2DES) in a classically strong magnetic field is a subject of current interest [1]. In conventional 2DES, current bias induced effects have been widely studied, in the context of the breakdown of quantum Hall effect [2,3], and of some recently discovered nonlinear phenomena such as the Zener-tunneling oscillations [4] and zero differential states [5]. Nevertheless, similar studies on 2DES with a relativistic-like linear energy dispersion, as recently realized in single layer graphene [6,7], are less reported.In this paper, we report on our experimental study on the influence of a relatively small dc bias on the magnetotransport of a single layer graphene. In the bias regime we explored (with current density up to 20 A/m), we find the magnetoresistance at lower field (B < 2 T) has negligible dependence on dc bias, while the Shubnikovde Haas (SdH) oscillations, occurring at higher fields, are obviously damped by increasing bias current. We show that the damping of the SdH oscillations can be well accounted for by an elevated electron temperature that is found to be linearly dependent on the bias current.Our most important findings, however, are from the differential resistance measurements, where a phase inversion of the SdH oscillations is observed with increasing the bias current. We observe the onset biasing current, at which a SdH maxima (minima) is about to invert to a minima (maxima), is linearly dependent on the magnetic field of the SdH extrema. These novel observations are quantitatively explained by taking into account the nonlinear response of the SdH, due to elevated electron temperatures by the biasing current.Data presented in this paper were measured on a lithographically defined Hall bar device of a single layer graphene, as shown in Fig. 1(a). The single layer graphene was mechanically exfoliated [6,7] from Kish graphite onto degenerately doped silicon substrate with a 300-nm thermal oxide SiO 2 . The Hall bar pattern was defined by electron-beam lithography (EBL) and oxygen plasma etching, with PMMA as a resist. Ohmic electrodes were defined by a second EBL, and by the subsequent 50nm-Pd deposition and lift-off...