Frequency hopping (FH) is a common characteristic of a wide variety of communication systems. On the other hand, software-defined radio (SDR) is an increasingly utilized technology for implementing modern communication systems. The main challenge when trying to realize an SDR FH system is the frequency tuning time, that is, the higher the hopping rate, the lower the required frequency tuning time. In this paper, significant universal hardware driver tuning options (within GNU Radio software) are investigated to discover the tuning option that gives the minimum frequency tuning time. This paper proposes an improved SDR frequency tuning algorithm for the generation of a target signal (with a given target frequency). The proposed algorithm aims to improve the frequency tuning time without any frequency deviation, thus allowing the realization of modern communication systems with higher FH rates. Moreover, it presents the design and implementation of an original GNU Radio Companion block that utilizes the proposed algorithm. The target SDR platform is that of the Universal Software Radio Peripheral USRP-N210 paired with the RFX2400 daughter board. Our results show that the proposed algorithm achieves higher hopping rates of up to 5,000 hops/second.