Transmission of dengue is a complex dynamic process. Dengue virus is transmitted to humans by the female Aedes aegypti mosquitoes. Dengue was first identified in Sri Lanka during 1960s and the risk due to dengue has increased rapidly during the past few decades mainly in the urban areas. There are several studies on dengue transmission based on mathematical and statistical models. However they are not capable of describing the complex dynamics of transmission since its transmission mechanism is highly dependent on various external factors such as climate, demography, geography and human mobility. Wavelet analysis is a powerful tool in mathematics, which can be used to reveal useful information of a highly non-stationary epidemiological time series. Wavelet theory can be used to obtain vital signals in a noisy epidemiological time series, which is useful to implement early warning systems to control the spread of epidemics. This particular study was aimed at investigating the applicability of wavelet theory to analyse dengue transmission in urban Colombo. The wavelet transformation was performed with data from weekly dengue cases time series from year 2006 to 2012 in the Colombo Municipal Council (CMC) area, and significant regions were observed in the spectrum that correspond to approximately 25 week cycles during the time period from year 2009 to 2012. The cross wavelet power spectrum showed that rainfall was leading the dengue cases in Colombo during the time period 2010 to 2012.