The microwave cavity experiment for the dark matter axion search is based on the theoretical prediction that axions could convert into microwave photons inside a High-Q cavity immersed in a strong magnetic field. In such experiments a weak, of order 10-22 W, quasi-monochromatic microwave signal should be detected by scanning it in a very wide frequency range. The best cryogenic semiconductor amplifiers have the lowest noise temperature plateau of about 1.0 K even at significantly lower ambient temperature. Superconducting quantum interference devices, or SQUIDs, can work as microwave amplifiers with temperature noise close to the standard quantum limit that is about 50 mK at 1 GHz [1]. Previously designed SQUID-based high frequency amplifiers have narrow bandwidth due to a microstrip resonant input coil. It requires serial replacements of SQUID preamplifiers in order to scan wide frequency range. This procedure is complex and time consuming because of a large mass of hardware should be cooled down below 100 mK. For suitable amplification at high frequency a SQUID should be designed with the smallest possible Josephson junction capacitance, reasonably low SQUID loop inductance, and maximal steepness of the transfer function. Sub-micron size cross-type Josephson junctions have a very low capacitance of about 0.04 pF that is one order smaller than a capacitance of Josephson junctions fabricated using conventional window-type technology. Such junctions initially were designed and used at IPHT for low-frequency SQUID current sensors [2]. Slightly modified current sensors were tested as amplifiers at frequency range 0.5 – 5 GHz. They showed high gain and both wideband and resonant performance. In this paper we describe wideband SQUID microwave amplifiers fabricated at IPHT using sub-micron size Josephson junctions with very low capacitance.