This work attempts to map aspherical velocities in the top 1200 km of the mantle that are illuminated by the International Seismological Centre P wave data. The processing includes summary ray sorting and hypocentral redetermination. To cope with the extreme variation of ray coverage, a multicell inversion is used to simultaneously constrain anomalies in overlapping cells. The multicell solutions are summed after inversion to form the final model, named P1200, at cell size of 1° × 1° and about 50 km in thickness. The lateral resolution of the model is about 1°–2° in major subduction zones and about 5°–15° in most places. Major features in the model withstood tests on signal coherency and different reference models. The long‐wavelength parts of the P1200 model correlate well with previous global models, especially the S12 model of shear wave. Among the large features in the transition zone and below, there are two fast bands, one from Canada to South America and another from Siberia, through East Asia and the Philippine Sea, to western Australia. There are also slow patches under the central Pacific and from India to eastern Africa. Though most subduction zones have slab‐like high‐velocity anomalies, they are sandwiched by broad slow velocities at shallow depths. Some of the slabs appear to penetrate the 660‐km discontinuity, and stagnant slabs are also seen in the transition zone. Plume‐like slow anomalies exist below some prominent hot spots like Hawaii, Iceland, Yellowstone, and French Polynesia.