An important and heretofore unresolved challenge in forestry has been how to project long-term tree growth (i.e., decades to hundreds of years) from short-term measurements (here 1 year) for trees that do not present annual growth rings in their trunk wood. Such a method is crucial in the lowland tropics, where few long-term growth measurements have been taken, and where frequently trees lack reliable annual growth rings because of the lack of winters or highly seasonal dry periods. The new piecewise linear (PL) growth model, developed in this article, relates logarithmic relative growth to trunk diameter. Having obtained the coefficients from piecewise linear regression, the long-term age-diameter curve is calculated, i.e., the expected average growth curve of a statistical population of individual trees. The model is applied to the following five tree species without annual growth rings from the tropical rainforest in Los Tuxtlas (Veracruz, Mexico): Aspidosperma megalocarpon, Cordia alliodora, Dialium guianense, Guarea grandifolia, and Persea schiedeana. Using the tools of multiple linear regression, the PL model is highly flexible to derive sigmoid, exponential, and over-exponential growth separately for different diameter segments.