Certain applications of superconducting quantum interference devices (SQUIDs) require a magnetic field measurement only in a very narrow frequency range. In order to selectively improve the alternating-current (ac) magnetic field sensitivity of a high-temperature superconductor SQUID for a distinct frequency, a single-coil LC resonant circuit has been used. Within the liquid nitrogen bath, the coil surrounds the SQUID and couples to it inductively. Copper coils with different numbers of windings were used to cover the frequency range from <1 to nearly 100 kHz. A superconducting coil made of YBa(2)Cu(3)O(7-delta) tape conductor was also tested. With the LC circuit, the signal-to-noise ratio of measurements could be improved typically by one order of magnitude or more in a narrow frequency band around the resonance frequency exceeding a few kilohertz. The best attained equivalent magnetic field resolution was 2.5 fT/radicalHz at 88 kHz. The experimental findings are in good agreement with mathematical analysis of the circuit with copper coil.