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A torsion-bar antenna (TOBA) is a low-frequency terrestrial gravitationalwave (GW) antenna which consists of two orthogonal bar-shaped test masses. Weupgraded the prototype TOBA and achieved the strain sensitivity $10^{-10}$Hz$^{-1/2}$ at around 1 Hz. We operated the upgraded TOBA (called the "Phase-IITOBA") located at Tokyo in Japan for 22.5 hours and performed an all-skycoherent search for continuous GWs using the $\mathcal{F}$-statistic. We placeupper limits on continuous GWs from electromagnetically unknown sources in thefrequency range from 6 Hz to 7 Hz with the first derivative of frequency lessthan $7.62 \times 10^{-11}$ Hz/s using data from the TOBA. As a result, nosignificant GW signals are found in the frequency band 6-7 Hz. The moststringent upper limit upper limit on the dimensionless GW strain with 95%confidence level in this band is $3.6 \times 10^{-12}$ at 6.84 Hz.

All-sky coherent search for continuous gravitational waves in 6-7 Hz band with a torsion-bar antenna