Positronium is an ideal system for the research of the quantum electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of positronium, $Delta_{mathrm{HFS}}$, gives a good test of the bound state calculations and probes new physics beyond the Standard Model. A new method of QED calculations has revealed the discrepancy by 15,ppm (3.9$sigma$) of $Delta_{mathrm{HFS}}$ between the QED prediction and the experimental average. There would be possibility of new physics or common systematic uncertainties in the previous all experiments. We describe a new experiment to reduce possible systematic uncertainties and will provide an independent check of the discrepancy. We are now taking data and the current result of $Delta_{mathrm{HFS}} = 203.395,1 pm 0.002,4 (mathrm{stat.}, 12,mathrm{ppm}) pm 0.001,9 (mathrm{sys.}, 9.5,mathrm{ppm}),mathrm{GHz} $ has been obtained so far. A measurement with a precision of $O$(ppm) is expected within a year.
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