A compact four-element dual-band multiple-input and multiple-output (MIMO) antenna system is proposed to achieve high isolation and low channel capacity loss. The MIMO antenna was designed and optimized to cover the dual-frequency bands; the first frequency band is a wide band, and it covers the frequency range of 1550–2650 MHz, while the other frequency band covers the 3350–3650 MHz range. The measured wide-band impedance bandwidths of 1.1 GHz and 300 MHz were achieved in the lower and upper frequency bands, respectively. The proposed structure consists of four novel antenna elements, along with a plus-sign-shaped ground structure on an FR4 substrate. The overall electrical size of the whole dual-band MIMO antenna system is $0.3\lambda$(W) × $0.3\lambda$(L) × $0.008\lambda$(H) for the lower frequency band. It achieved greater than 10 and 19 dB isolation in the lower and upper frequency bands, respectively. The antenna system accomplished an envelope correlation coefficient of $\left|\rho \right|\le 0.08$ in the lower frequency band, while it achieved $\left|\rho \right|\le 0.02$ in the higher frequency band. The computed channel capacity loss remained less than almost 0.4 bits/s/Hz in both frequency bands. Therefore, it achieved good performance in both frequency bands, with the additional advantage of a compact size. The proposed MIMO antenna is suitable for compact handheld devices and smartphones used for GSM (Global System for Mobiles), UMTS (Universal Mobile Telecommunications Service), WCDMA (Wideband Code Division Multiple Access), LTE (Long Term Evolution), 5G sub-6 GHz, PCS (Personal Communications Service), and WLAN (wireless local area network) applications.