"When pushed to its limits, the rear of the GX "slid out until the vehicle was almost sideways before the electronic stability control system was able to regain control," the magazine reported.
"We believe that in real-world driving, that situation could lead to a rollover accident, which could cause serious injury or death," it said.
Toyota says it has not experienced any similar problems in its own tests.
"Our engineering teams are vigorously testing the GX using Consumer Reports' specific parameters to identify how we can make the GX's performance even better," the company said.
A Toyota spokeswoman said a number of tests are now being conducted on all the company's sport utility vehicles models, including Land Cruisers and Sequoias.
"The foremost reason for doing the extra tests is to put customers' minds at ease," Ririko Takeuchi, the spokeswoman, said.
Toyota has sold about 5,400 of the Lexus GX 460 SUVs in the four months it has been on the market.
But even though the vehicle is not a high-volume model, analysts say the concerns could be another blow to the reputation of Toyota and its luxury car brand.
"Even though the vehicle's volume is a relatively small part of [Toyota's] sales, as Toyota's quality issues are now affecting Lexus too, we think the cost to repair the dented brands is poised to rise," Efraim Levy, an S&P equity analyst, said.
Toyota has recalled more than nine million vehicles worldwide, including more than six million in the United States since late 2009, mainly for acceleration problems but also for some faulty brakes on some hybrid vehicles.