We present a Gear-type code that efficiently solves ordinary differential equations in large grid-domains. To obtain the final code, we modified an original program of C.W. Gear, built and added a sparse-matrix package, and vectorized all loops about the grid-cell dimension. Furthermore, to obtain at least 90% vectorization potential while preventing equations in some regions of the grid from slowing the solution over the entire grid-domain, we divided the domain into blocks of grid-cells and vectorized around these blocks. The sparse-matrix solution reduced the average number of LU-decomposition calculations, compared to a full-matrix solution, by factors of between 20 (for a matrix of order 40) and 120 (for a matrix of order 90). It also reduced both back-substitution calculations and total array space by factors of between 5 and 12 for the above matrix sizes. Vectorization on a CRAY-90 computer increased the speed by another factor of about 120 over the code running in scalar form. We tested the speed and accuracy of the program for several chemical applications on a single processor of the CRAY-90 computer. The code averaged between 1 and 2 min of computer time per day of simulation to solve a smog-chemistry set of 92 specied and 222 reactions over a 10,000-cell grid, with continuously changing photorates. It also took 3-4 min per day to solve a stratospheric-chemistry set of 39 species and 108 reactions over a 100,000-cell grid. In addition, we tested the speed of the code while it solved aqueous chemistry in 43 aerosol size bins, along with other physical processes and transport, over a large grid. Finally, we compared the speed and other statistics from SMVGEAR to those of an existing sparse matrix Gear code, LSODES, and to a new method that we call the Multistep Implicit-Explicit (MIE) method.