We established a permanent plot located at Picealikiangensis forest in Shangri-La county, northwest of Yunnan province, China, from 2008 to 2012, and recorded all stems with the diameter at breast height (DBH) ≥5 cm, mapped the positions of corresponding stem bases. Because Picealikiangensis (Franch.) Pritz. Was a dominant species, it was specifically measured. We used Bayesian statistical approach to quantify a spatially autocorrelated random effects. Meanwhile, the effect of competition on individual growth was also considered. The results showed that symmetrical competition played a very important role in affecting individual growth. When spatially autocorrelated random effects were included, the model accounted for a significant proportion of the variation (R2 = 0.87; P< 0.001). We also analyzed collected data of other tree species found in the plot, and a high level of correlation relationship was consistently found when spatial autocorrelation was included. The Bayesian approach used in this study, including the intrinsic CAR model, is a powerful technique for exploring important ecological information from forest census data. Our model for the measurement of tree growth rate may be used to simulate forest dynamics and to improve the management practices of natural forests.