In this paper, we use a machine-learning method, random forest (RF), to identify reliable members of the old (4Gyr) open cluster M67 based on the high-precision astrometry and photometry taken from the second Gaia data release (Gaia-DR2). The RF method is used to calculate membership probabilities of 71117 stars within 2.5{deg} of the cluster center in an 11-dimensional parameter space, the photometric data are also taken into account. Based on the RF membership probabilities, we obtain 1502 likely cluster members (>=0.6), 1361 of which are high-probability cluster members (>=0.8). Based on high-probability memberships with high-precision astrometric data, the mean parallax (distance) and proper-motion of the cluster are determined to be 1.1327+/-0.0018mas (883+/-1pc) and (<{mu}_{alpha}_cos{delta}>,<{mu}_{delta}_>)=(-10.9378+/-0.0078,-2.9465 +/-0.0074)mas/yr, respectively. We find the cluster to have a mean radial velocity of +34.06+/-0.09km/s, using 74 high-probability cluster members with precise radial-velocity measures. We investigate the spatial structure of the cluster, the core and limiting radius are determined to be 4.80'+/-0.11' (~1.23+/-0.03pc) and 61.98'+/-1.50' (~15.92+/-0.39pc), respectively. Our results reveal that an escaped member with high membership probability (~0.91) is located at a distance of 77' (~20pc) from the cluster center. Furthermore, our results reveal that at least 26.4% of the main-sequence stars in M67 are binary stars. We confirm that significant mass segregation has taken place within M67.