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As a power class of generalization of Einstein’s general relativity, the R 1 + δ gravity is confronted with planetary motions in the solar system. Using the supplementary advances in the perihelia provided by current INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain new upper limits on δ in the solar system when the Lense–Thirring effect due to the Sun’s angular momentum and the uncertainty of the Sun’s quadrupole moment are properly taken into account. These two factors were mostly absent in previous works dealing with δ . We find that INPOP10a yields the upper limit as δ = ( 0.6 ± 4.4 ) × 10 - 24 and EPM2011 gives δ = ( 7.5 ± 3.4 ) × 10 - 24 . Both of them are improved by about 5 orders of magnitude than previous result. [ABSTRACT FROM AUTHOR]