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The China BeiDou global navigation satellite system (BDS-3) has started to provide free and open precise positioning services to users in China and surrounding areas since Jul 2020 on the GEO B2b signal. The initial assessment of BDS-3 PPP-B2b products and the PPP performance over a period of near five months from Jul 26, 2020 to Dec 19, 2020 was carried out in this work. Taking the GBM products as a reference, the average signal-in-space ranging error (SISRE) of the disseminated orbit and clock products is approximately 82.3 cm (RMS) and 3.9 cm (STD) for BDS-3 satellites, and about 135.8 cm (RMS) and 7.5 cm (STD) for GPS. The average positioning error RMS at six permanent stations in China is about 2.1 (1.8) and 2.6 (2.1) cm in the horizontal and vertical components respectively for BDS-only (BDS + GPS) static PPP. In the kinematic PPP mode, the average positioning error (95%) at the same six stations is about 21.5 (15.2) and 33.4 (30.3) cm in the horizontal and vertical component respectively for BDS-only (BDS + GPS), with an average convergence time of 17.4 (16.2) min. In addition, two vehicle-based kinematic PPP tests show average position error (95%) of about 23.5 (18.6) and 48.8 (37.1) cm in horizontal and vertical respectively, and an average convergence time of 10.4 (14.2) min for BDS-only (BDS + GPS) PPP. The assessment results are overall in accordance with the official claim of centimeter-level in static mode and decimeter-level in kinematic mode from BDS-3 PPP service. [ABSTRACT FROM AUTHOR]