Biomass may be converted to useful energy via pyrolysis, gasification, and liquefaction. The primary factors that affect the distribution of product profiles during the pyrolysis are temperature, heating rate, catalyst, residence time, and ratio between volatile matter and fixed carbon. In this work, the pyrolysis of leaves and stem of Nerium oleander was carried out in a laboratory scale fixed-bed reactor in the temperature range of 250–650 °C for 1000-μm particles at atmospheric pressure with and without Zeolite-5A as a catalyst. The pyrolysis products were measured in three different phases, namely, gas, liquid/tar, and char. The yield of liquid product varied from 7.4% to 41.3% of 1000-μm particles of leaves and stem of N. oleander at a 10 °C/min heating rate for non-catalytic and catalytic pyrolysis. The optimal temperature for higher liquid product yield was observed to be in the range of 370–450 °C. We conclude that higher hemicellulose as well as a higher VM- to -FC ratio results in higher liquid product yield during pyrolysis. Compared to the non-catalytic pyrolysis, the liquid product yield is 1.4 times higher for catalytic pyrolysis. The liquid product yield with Zeolite-5A was found to be much higher when compared to other zeolite catalysts. Therefore, Zeolite-5A may be used as a catalyst for biomass pyrolysis with reduced char production.